can someone help me with these motion problems please A boy throws a stone strai

Question

can someone help me with these motion problems please

A boy throws a stone straight upward with an initial speed of 17 m/s near the surface of the Earth. What maximum height above the starting point will: stone reach before falling back down? m A golf ball is hit with an initial speed of 39.0 m/s at an angle of 34degree above the horizontal. Find the highest point reached by the golf ball, m A girl throws a rock horizontally with a velocity of 13.5 m/s from a bridge. It falls 24.0 m to the water below. How far from the bridge does the rock ?(horizontal distance)(g = 9.8 m/s^2)

Explanation / Answer

1)energy conservation shall apply :
m*Voy^2 = 2*m*g*hmax....Voy being the initial vertical speed
m cross
hmax = Voy^2/2g = 17^2/2*9.8 = 14.73 m

2) time will the ball spend in the air?

assuming it is launched close to the ground.

time of flight = t = 2(vertical velocity/g)

vertical velocity = (39)sin34° = 21.80 m/s

therefore t = 2(21.80/9.81) = 4.44 s

how far will the golf ball fly?

R = range = horizontal distance

=> R = horiz. velocity * time of flight

= (39)cos34° x 4.44 = 143.556m

3)We will use the equation of motion:

X(t) = Xo + Vo + (1/2)*a*t^2 twice
where Xo = initial distance
Vo = initial velocity
a = acceleration

first we will use it in the Y direction to find how long it takes to fall that far
it starts out 24 meters up so Yo = 24
but has no initial velocity in this direction so Vo = 0
so
Y(t) = 24 + 0 + (1/2)*g*t^2 (g = acceleration due to gravity g = -9.8)
so 24= 4.9 * t^2
t = 2.1 seconds

now we will use it in the X direction to find out how far it travels in that time
it has no initial displacement in the X direction
it also has no acceleration in the X direction (neglecting air resistance)
it does have an initial velocity in this direction of Vo = 10m/s
X(t) = 0 + Vo*t + 0
so the total distance is X(t) = 13.5m/s * 2.1 sec
X(t) = 28.35 meters before it hits the water

Calculation may be wrong but concept is right

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