1. Aurora hit a baseball with an initial velocity of 70 feet per second at an angle of 30° with the horizontal. The ball hit her bat when the ball was 3 feet above the ground.
A) No one interferes with the ball. How long does it take the ball to hit the ground? Round your answer to the nearest hundredth of a second. Show all your work.
B) How far did the ball travel horizontally? Use your answer from Part (a) in your calculations. Round your answer to the nearest tenth of a foot. Show all your work.
The vertical position is given by
yf = yo + vot - 1/2 a t^2 yo = 3 vo = 70 sin 30 = 35 f/s a = -32.174 ft/s^2
when the ball hits the ground yf= 0 so you have
0 = 3 + 35 t - 1/2 (32.174)t^2 solve to find t
the x component of the velocity is 70 cos 30 = 60.62 f/s
use the 't' you found above to find the x distance = 60.62 * t