Question

A major leaguer hits a baseball so that it leaves the bat at a speed of 31.5 m/s and at an angle of 34.9 ? above the horizontal. You can ignore air resistance.

1.)

At what two times is the baseball at a height of 10.0 m above the point at which it left the bat?

2.)

Calculate the horizontal component of the baseball's velocity at each of the two times you found in part (a).

Please enter your answer as two numbers, separated with a comma, in order v1, v2.

3.)

Calculate the vertical component of the baseball's velocity at each of the two times you found in part (a).

Please enter your answer as two numbers, separated with a comma, in order v1, v2.

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

5.)

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

This was all the information given

Answer 1

The base ball leaves the bat at velocity 'V' =31.5 m/s at an angle 34.9degree with horizontal at the level at which it left the bat.

So there will be two components of 'V'

1.) Vertical component =V1 = V sin 34.9= 18.02 m/s

2.) Horizontal Component=V2= V cos34.9= 25.83 m/s

Note: the Horizontal component:V2 will be always Constant =25.83m/s as there is no acceleration/deceleration towards horizontal movement.

The vertical Component will take the ball to a height vertically.

Initial velocity of Ball vertically=18.02m/s

h=10m, a= -g= -9.8m/s^2

h=vt+1/2 at^2

10=18.02t-4.9t^2

4.9t^2+10-18.02t=0

solving quadratically:

t=0.68107 or 2.9965 sec.

1) t= 0.68107s and 2.9965s at height 10m above the level at which it was hit by the bat.

2)Horizontal components of the velocity=25.83m/s both the cases.

3) During ascending the vertical component: Vy = V1-gt=18.02-9.8*(0.68107)=11.35 m/s

During descending: Vertical component= -Vy = -11.35m/s

4) the Magnitude of the velocity at the level it was hit by the ball is same as it was leaving the ball= 31.5m/s

5) the Magnitude of the velocity at the level it was hit by the ball is same as it was leaving the ball= 30m/s

and direction/angle at which it will reach there is 34.9 degree clock wise.