Question

Emily throws a soccer ball out of her dorm window to Allison, who is waiting below to catch it. Emily throws the ball at an angle of 30° below horizontal with a speed of 12 m/s, and Allison catches it 2.5 s later. How far from the base of the dorm does Allison stand to catch the ball, in meters? Use g = 10.0 m/s2.

Answer 1

Answer:30 meters

Explanation:To find the horizontal distance at which Allison stands to catch the ball, we can use the horizontal motion equation: Distance = velocity x time Since the ball is thrown at an angle below horizontal, we need to find the horizontal component of the velocity. The horizontal component can be found using the trigonometric function cosine: Horizontal velocity = initial velocity x cosine(angle) So the horizontal velocity is 12 m/s * cosine(30°). After finding the horizontal velocity, we can use it in the horizontal motion equation: Distance = horizontal velocity x time Distance = (12 m/s * cosine(30°)) * 2.5 s Therefore, the distance from the base of the dorm where Allison stands to catch the ball is 30 meters.