If a rocket launches at an angle of 30 degrees to the horizontal and reaches a h

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What’s inside this PDF?

Question: If a rocket launches at an angle of 30 degrees to the horizontal and reaches a height of 1,000 meters, what is the horizontal distance covered by the rocket?

Options:

1,732 m
1,000 m
1,500 m
2,000 m

Correct Answer: 1,732 m

Solution:

Horizontal distance = Height / tan(30°) = 1,000 m / (√3/3) = 1,732 m.

If a rocket launches at an angle of 30 degrees to the horizontal and reaches a h

Practice Questions

If a rocket launches at an angle of 30 degrees to the horizontal and reaches a height of 1,000 meters, what is the horizontal distance covered by the rocket?

1,732 m
1,000 m
1,500 m
2,000 m

Questions & Step-by-Step Solutions

If a rocket launches at an angle of 30 degrees to the horizontal and reaches a height of 1,000 meters, what is the horizontal distance covered by the rocket?

Step 1: Understand that the rocket's launch angle is 30 degrees to the horizontal.
Step 2: Know that the height reached by the rocket is 1,000 meters.
Step 3: Use the tangent function, which relates the height and horizontal distance in a right triangle. The formula is: Horizontal distance = Height / tan(angle).
Step 4: Substitute the values into the formula: Horizontal distance = 1,000 m / tan(30°).
Step 5: Calculate tan(30°). The value of tan(30°) is √3/3.
Step 6: Replace tan(30°) in the formula: Horizontal distance = 1,000 m / (√3/3).
Step 7: To divide by a fraction, multiply by its reciprocal: Horizontal distance = 1,000 m * (3/√3).
Step 8: Simplify the calculation: Horizontal distance = 1,000 m * (3/√3) = 1,732 m.

Projectile Motion – Understanding the relationship between vertical height and horizontal distance in projectile motion, particularly using trigonometric functions.
Trigonometry – Applying the tangent function to relate angles and sides in right triangles.

If a rocket launches at an angle of 30 degrees to the horizontal and reaches a h

What’s inside this PDF?

If a rocket launches at an angle of 30 degrees to the horizontal and reaches a h

Practice Questions

Questions & Step-by-Step Solutions

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