A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40$\degree$ angle to the ground.The magnitude of the vertical impulse the catapult receives from the rock is A)5.1 * 10⁴ N . s. B)6.1 *10⁴ N . s. C)8.0 * 10⁴ N . s. D)5.0 * 10⁵ N . s. E)6.0 * 10⁵ N . s.

Question

Quizplus · Accepted Answer

The vertical component of the initial velocity is 100sin(40°) ≈ 64.3 m/s. Using the principle of conservation of momentum, we know that the impulse the catapult receives from the rock equals the impulse the rock receives from the catapult, but with the opposite sign. The impulse equals the change in momentum, which is the mass times the change in velocity. In the vertical direction, the change in velocity is equal to the initial vertical component of the velocity, since there is no acceleration in the vertical direction (assuming air resistance is negligible). Therefore, the magnitude of the vertical impulse the catapult receives is:
|Impulse| = |−(800 kg)(64.3 m/s)| = 5.1 × 1014 N·s.

A Catapult Fires an 800-Kg Rock with an Initial Velocity °\degree°

A Catapult Fires an 800-Kg Rock with an Initial Velocity $\degree$