projectile motion

Question

A baseball player hits a home run over the left-field fence, which is 105 m from home plate. The ball is hit at a point 1.00m directly above home plate, with an initial velocity directed 31.0º above the horizontal. By what distance does the baseball clear the 2.00 m high fence, if it passes over it 3.10 s after being hit?

Answer 1

You can find the average horizontal velocity of the ball leaving the bat assuming no horizontal acceleration that is also the initial horizontal velocity of the ball (Δx/Δt) (105m/3.10s).

Knowing the initial angle and the horizontal velocity which does not change you can determine the initial vertical velocity (tan 31.0^o= v_yo/v_xo).

The vertical position of the ball at 3.10 s (at the 2 m high fence) can now be determined:

y=1/2a_yt²+ v_oyt + y_o where a_y = -9.8 m/s² assuming free fall conditions and y_o = 1.0m.

If y computed is greater than 2.0 m you will have proved the ball clears the fence. It’s up to you to input the data and find your answer.

Draw pictures to include the information given and the unknowns.

Good luck.