Calculating Trajectory Motion of Ball Hit at 40.0m/s

[p47n15]

A baseball is hit by a bat and given a velocity of 40.0m/s at an angle of 30 deg above the horizontal. The height of the ball above the ground upon the impact with the bat is 1.0m.

(a) What maximum height above the ground does the ball reach?
(b) A fielder is 110.0m from homeplate when the ball is hit and the ball's trajectory is directly at him. If he begins running at the moment the ball is hit and catches the ball when it is still 3.0 m above the ground, how long does he run before catching the ball?
(c) How fast (average speed) does he have to run in order to catch the ball ?

 

[berkeman]

Welcome to the PF. You must show us the relevant equations and your attempt at the solutions before we can offer any tutorial help. Those are the PF Rules (see the "Rules" link at the top of the page).

So, what general equations do you think you would use for this type of problem, and how would you approach question (a)?

 

[p47n15]

for (a)

v= 40 sin 30

initial v = 20m/s g= 9.8 m/s^2 final v = 0

(v)^2 final = (v)^2 initial + 2gd

 

[berkeman]

for (a)

v= 40 sin 30

initial v = 20m/s g= 9.8 m/s^2 final v = 0

(v)^2 final = (v)^2 initial + 2gd

40 sin 30 is the initial vertical velocity. What is the equation for the vertical v(t), in terms of the initial y position, initial vertical velocity, and the acceleration of gravity? What can you solve for using this equation?