Question

A baseball is hit from a height of 4 feet above the ground with an initial velocity of 110 feet per second and at an angle of 35 ° above the horizontal. Find the maximum height reached by the baseball. Determine whether it will clear a 10-foot-highfence located 375 feet from home plate. Use the model for projectile motion, assuming there is no air resistance.

Answer 1

Answer:

Part a)

$h = 62.2 ft$

Part b)

It will not able to cross the pole

Explanation:

As we know that ball is hit with speed of 110 ft/s at an angle of 35 degree

so here we will say

$v_y = 110 sin35$

$v_x = 110 cos35$

now at the maximum height the vertical velocity will become zero

so here we can use kinematics

$v_f^2 - v_y^2 = 2 a h$

here we have

$a = -32 ft/s^2$

$v_f = 0$

$v_y = 63.1 ft/s$

now we have

$0 - 63.1^2 = 2(-32)h$

$h = 62.2 ft$

Part b)

now the height of ball is related to the distance from point of projection is given as

$y = xtan\theta - \frac{gx^2}{2v^2cos^2\theta}$

now we know that

$x = 375 ft$

$y = 375(tan35) - \frac{(32)(375^2)}{2(110^2)(cos35)^2}$

$y = 262.6 - 277.12 = -14.5 ft$

since its coming negative so it will not able to cross the pole