AP Physics Question?

Question

A person standing at the top of a hemispherical rock of radius R = 13.00 m kicks a ball (initially at rest on the top of the rock) to give it horizontal velocity vi as in Figure P4.62.

Figure P4.62

(a) What must be its minimum initial speed if the ball is never to hit the rock after it is kicked?
m/s
(b) With this initial speed, how far from the base of the rock does the ball hit the ground?

Answer 1

Using the equations of motion:
x(t)=vi*t
y(t)=26-.5*g*t^2

When y(t)=13, x(t)>13

13 13=26-.5*g*t^2

vi>sqrt(9.81*13/2)
vi>7.99

if vi=7.99, then the ball will land
0=26-.5*g*t^2
t=sqrt(52/9.81)
landing is vi*t or 18.4 m


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