A major leaguer hits a baseball so that it leaves the bat at a speed of 29.2m/s

Question

A major leaguer hits a baseball so that it leaves the bat at a speed of 29.2m/s and at an angle of 36.6 degrees above the horizontal. You can ignore air resistance.

Part A

At what two times is the baseball at a height of 10.1m above the point at which it left the bat?

Give your answers in ascending order separated with comma.

t(1),t(2)= ....... , ......

Part B

Calculate the horizontal component of the baseball's velocity at the earlier of the two times calculated in part (a).

v(x)=.........(m/s)

Part C

Calculate the vertical component of the baseball's velocity at the earlier of the two times calculated in part (a). Assume that UP is the positive vertical direction.

v(y)= .......... (m/s)

Part D

Calculate the horizontal component of the baseball's velocity at the later of the two times calculated in part (a).

v(x)= ......... (m/s)

Part E

Calculate the vertical component of the baseball's velocity at the later of the two times calculated in part (a). Assume that UP is the positive vertical direction.

v(y)= ........... (m/s)

Part F

What is the magnitude of the baseball's velocity when it returns to the level at which it left the bat?

v= .......... (m/s)

Part G

What is the direction of the baseball's velocity when it returns to the level at which it left the bat?

Theta= ............ degrees below the horizontal.

..................

Please show work if possible. Thank you

Explanation / Answer

A. h = uy*t + at^2 /2

10.1 = 29.2sin36.6*t - 9.8t^2 /2

4.9t^2   - 17.41t + 10.1 = 0

on solving t = 0.730 sec , 2.82 sec ,

B)     
v(x) is always same throuout the motion
v(x) = 29.2cos36.6 =23.44 m/s

c) v(y) = 29.2sin36.6 - 9.8 t
           = 17.41 - 9.8x0.73 = 10.26 m/s

D) v(x) is always same throuout the motion
v(x) = 29.2cos36.6 =23.44 m/s

e) )

v(y) = 29.2sin36.6 - 9.8 t
           = 17.41 - 9.8x2.82 = - 10.26 m/s

f) according energy conservation theorem.

there is no loss or gain in potential energy ( as initially and finally at same verical elevel)

so speed will be same = 29.2 m/s

g) direction will be just opposite.
= 36.6 degree below horizontal.

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