Vectors and Projectile Motion

Question

A baseball is hit from a bat at 37m/s at an angle of 40°to the horizontal . It travels towards the outfield fence,which is 130m away. Does the baseball make it over the 3m high fence? If it does how high above the fence it pass?

Answer 1

Let us find the Horizontal range

R = V² Sin 2 theta/ g = 37*37 *Sin 80/ g = 37*37* Sin 80/9.8 = 137 .57 m, This is More than distance of fence

V= 37 m/s , g= 9.8

Now let us find height it crosses at fence

x = 130 m, y = ?

Use equation of projectile

y = V Sin theta -1/2 (gt² )

and X = (V Cos theta) /t

t = X /V Cos theta

t = 130/V Cos 40 = 130/VCos 40 = 169.71/ 37 = 4.59 sec sec

Plug in this to get Y

Y =X * tan theta - 1/2 (gX² )/ V² Cos ² 40

3 m fence at 130 away as height here is 6 m aaprox