physics problems kinematics

Question

Vivian and Meguin, who are both 1.575m tall, are playing around throwing small yellow balls as far as they can. Meguin throws as hard as she can to try and hit Vivian with the ball, who is 4.00 meters in front of Meguin. Because Meguin is an AP Physics student, she is only capable of throwing at a max velocity of 5.50 m/s. If Meguin throws with all her might at an angle 35.0 degrees from 1.80 m above the ground, where will the ball make first contact? If the ball does not hit Vivian, how many meters in front or behind Vivian will the ball hit the floor. If the ball does hit Vivian, how many meters above the ground does the ball make contact with Vivian? Leave your answer in 'm' with direction as 'in front of' of 'behind' Vivian if the ball misses, or 'above the ground' if the ball hits.

BONUS. Ellen flies a cargo plane at a constant speed of 140. m/s at an angle 40.0 degrees above the horizontal. When Ellen gets to a height of 50.0 m, he releases a supply package is out of the bottom of the plane at time t=0. Exactly two seconds later, a second package is dropped out of the bottom of the plane. Air resistance is negligible. How far apart will the packages land on the ground? round your answer to 3 s.f. and do not use scientific notation.

Yuna tries to get her V5 Pro G golf ball out of a bunker, which is located 5.00 m below the level green surface. She hits the ball with an initial velocity of 15.0 m/s at an angle of 60.0 degrees above the horizontal. What is the velocity of ball as it reaches out of the bunker right before it hits the level green? Give direction 'at x degrees relative to the horizontal'

Answer 1

Begin by using the kinematics formula d = v_it + 1/2 at², along with the information given, to write expressions for the vertical and horizontal positions of the ball as functions of time. You will need to resolve the initial velocity into x and y components, and note that accelerations are g vertically and 0 horizontally.

Horizontally, x - x_i = v_it + 1/2 at² becomes x(t) = 4.5 t. Vertically, y(t) = 1.8 + 3.2 t - 4.9 t².

The ball will follow a parabolic trajectory. We don't yet know whether this trajectory will intersect the ball in front of Vivian, cross Vivian's body, or go above her head. Find the time required for the ball to travel horizontally for 4.0 m (set x = 4 and solve for t), and then determine the vertical position of the ball at that time. If you find that y is between 0 and 1.575, then the ball hits Vivian. For y less than 0, the ball hit the floor in front of Vivian. For y greater than 1.575, it went over her head.