Question

A batted baseball is hit with a velocity of 42.1 m/s, starting from an initial height of 7 m. Find how high the ball travels in two cases:

(a) a ball hit directly upward and

(b) a ball hit at an angle of 75° with respect to the horizontal.

Also find how long the ball stays in the air in each case.

case A

case b

Answer 1

1)

a)

In case A, vertical component of initial velocity is 42.1 m/s

vf = 0 m/s

a = -9.8 m/s^2

use:

vf^2 = vi^2 + 2*a*(h-ho)

0 = 42.1^2 + 2*(-9.8)*(h-7)

(h-7)= 90.4

h = 97.4 m

Answer: 97.4 m

b)

In case B, vertical component of initial velocity is 42.1*sin 75 = 40.7 m/s

vf = 0 m/s

a = -9.8 m/s^2

use:

vf^2 = vi^2 + 2*a*(h-ho)

0 = 40.7^2 + 2*(-9.8)*(h-7)

h-7= 84.5

h = 91.5 m

Answer: 91.5 m

2)

a)

vf = vi + a*t

0 = 42.1 - 9.8*t

t = 4.30 s

Answer: 4.30 s

b)

vf = vi + a*t

0 = 40.7 - 9.8*t

t = 4.15 s

Answer:4.15 s