A dynamics problem uses Projectile range. Given launch speed (v0) = 41.0000 m/s; launch angle (theta) = 61.0000 deg, determine the range (R) in m.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch speed (v_{0}) = 41.0000 m/s, launch angle (theta) = 61.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 145.3\ \text{m}$$

6. Step 6 — Check: returning R = 145.3 m to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 290.6 — kept a factor of two that cancels in the correct rearrangement.
• 72.6590 — dropped that same factor in the other direction.
• 159.8 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch angle (theta) = 67.0000 deg; range (R) = 134.5 m, determine the launch speed (v0) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except v0 is given, so isolate v0 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that v0 stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch angle (theta) = 67.0000 deg, range (R) = 134.5 m$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$v_{0} = 42.8281\ \text{m/s}$$

6. Step 6 — Check: returning v0 = 42.8281 m/s to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 85.6562 — kept a factor of two that cancels in the correct rearrangement.
• 21.4140 — dropped that same factor in the other direction.
• 47.1109 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch speed (v0) = 16.5000 m/s; launch angle (theta) = 65.0000 deg, determine the range (R) in m.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch speed (v_{0}) = 16.5000 m/s, launch angle (theta) = 65.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 21.2595\ \text{m}$$

6. Step 6 — Check: returning R = 21.2595 m to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 42.5190 — kept a factor of two that cancels in the correct rearrangement.
• 10.6297 — dropped that same factor in the other direction.
• 23.3854 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch angle (theta) = 27.0000 deg; range (R) = 18.8000 m, determine the launch speed (v0) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except v0 is given, so isolate v0 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that v0 stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch angle (theta) = 27.0000 deg, range (R) = 18.8000 m$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$v_{0} = 15.0985\ \text{m/s}$$

6. Step 6 — Check: returning v0 = 15.0985 m/s to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 30.1971 — kept a factor of two that cancels in the correct rearrangement.
• 7.5493 — dropped that same factor in the other direction.
• 16.6084 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch speed (v0) = 46.0000 m/s; launch angle (theta) = 11.0000 deg, determine the range (R) in m.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch speed (v_{0}) = 46.0000 m/s, launch angle (theta) = 11.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 80.8020\ \text{m}$$

6. Step 6 — Check: returning R = 80.8020 m to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 161.6 — kept a factor of two that cancels in the correct rearrangement.
• 40.4010 — dropped that same factor in the other direction.
• 88.8822 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch angle (theta) = 60.0000 deg; range (R) = 128.4 m, determine the launch speed (v0) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except v0 is given, so isolate v0 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that v0 stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch angle (theta) = 60.0000 deg, range (R) = 128.4 m$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$v_{0} = 38.1375\ \text{m/s}$$

6. Step 6 — Check: returning v0 = 38.1375 m/s to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 76.2749 — kept a factor of two that cancels in the correct rearrangement.
• 19.0687 — dropped that same factor in the other direction.
• 41.9512 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch speed (v0) = 34.5000 m/s; launch angle (theta) = 16.0000 deg, determine the range (R) in m.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch speed (v_{0}) = 34.5000 m/s, launch angle (theta) = 16.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 64.2953\ \text{m}$$

6. Step 6 — Check: returning R = 64.2953 m to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 128.6 — kept a factor of two that cancels in the correct rearrangement.
• 32.1476 — dropped that same factor in the other direction.
• 70.7248 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch angle (theta) = 44.0000 deg; range (R) = 268.9 m, determine the launch speed (v0) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except v0 is given, so isolate v0 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that v0 stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch angle (theta) = 44.0000 deg, range (R) = 268.9 m$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$v_{0} = 51.3762\ \text{m/s}$$

6. Step 6 — Check: returning v0 = 51.3762 m/s to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 102.8 — kept a factor of two that cancels in the correct rearrangement.
• 25.6881 — dropped that same factor in the other direction.
• 56.5139 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch speed (v0) = 29.0000 m/s; launch angle (theta) = 65.0000 deg, determine the range (R) in m.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except R is given, so isolate R symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that R stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch speed (v_{0}) = 29.0000 m/s, launch angle (theta) = 65.0000 deg$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$R = 65.6721\ \text{m}$$

6. Step 6 — Check: returning R = 65.6721 m to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 131.3 — kept a factor of two that cancels in the correct rearrangement.
• 32.8361 — dropped that same factor in the other direction.
• 72.2393 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion

A dynamics problem uses Projectile range. Given launch angle (theta) = 19.0000 deg; range (R) = 253.2 m, determine the launch speed (v0) in m/s.

Start with the thinking

• The governing relation printed in this handbook section is Projectile range.
• Everything except v0 is given, so isolate v0 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Dynamics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$R = v_0^2 \sin(2\theta) / g$$

2. Step 2 — Rearrange the relation so that v0 stands alone on the left-hand side.

3. Step 3

   $$List the givens: launch angle (theta) = 19.0000 deg, range (R) = 253.2 m$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$v_{0} = 63.5178\ \text{m/s}$$

6. Step 6 — Check: returning v0 = 63.5178 m/s to

   $$R = v_0^2 \sin(2\theta) / g$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 127.0 — kept a factor of two that cancels in the correct rearrangement.
• 31.7589 — dropped that same factor in the other direction.
• 69.8696 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Dynamics → Projectile Motion