A boy throws a rock with an initial velocity of 2.15 m/s at 30.0° above the horizontal. If air resistance is negligible, how long does it take for the rock to reach the maximum height of its trajectory?
A) 0.110 s
B) 0.194 s
C) 0.215 s
D) 0.303 s

Question

Quizplus · Accepted Answer

The vertical component of the initial velocity is:$$v_{y,i} = v_i \sin 	heta = (2.15 	ext{ m/s}) \sin 30.0° = 1.075 	ext{ m/s}$$The acceleration due to gravity is:$$a_y = -g = -9.81 	ext{ m/s}^2$$The time it takes for the rock to reach the maximum height of its trajectory is:$$v_{y,f} = v_{y,i} + a_y t$$$$0 = 1.075 	ext{ m/s} + (-9.81 	ext{ m/s}^2) t$$$$t = \frac{1.075 	ext{ m/s}}{9.81 	ext{ m/s}^2} = 0.110 	ext{ s}$$

A Boy Throws a Rock with an Initial Velocity of 2.15