A batter hits a baseball with an initial horizontal speed of $76$ mph and an initial rate of climb of $63$ mph $.$

a$.$ Start by drawing the vectors involved, then draw the component vector showing the baseball's speed and direction when it leaves the bat. Have you done this? $$

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b$.$ How fast is the ball traveling when it leaves the bat?

$$ mph $$

c$.$ When the ball leaves the bat, what angle does it initially form with the horizon?

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d$.$ In this context, gravity will change the ball's rate of climb over time but has no effect on the ball's horizontal speed. If the ball lands $2\mathrm{.}941$ seconds after it was hit, how many feet did the ball travel? $($Recall that there are $5,280$ feet in one mile and $3600$ seconds in one hour.$)$

$$ feet $$