Physics help?

Question

I have three questions i'm stuck on, please help.

1) A pool ball leaves a 0.60-meter high table with an initial horizontal velcity of 2.4m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table's edge and the ball's landing location.

2)A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

3)A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degress above the horizontal. Determine the time of flight, the horizontal distance, and the peak height of the long-jumper.

Answer 1

1)
the fall will follow
y(t)=0.6-.5*9.8*t^2
solve for t when y(t)=0
0.35 sec
in that time, the ball will travel horizontally
x(t)=2.4*t
x(0.35)=2.4*0.35
0.84 m

2) is similar
y(t)=22-.5*9.8*t^2
when the ball hits
t=sqrt(22/(.5*9.8))
2.12 sec
x(t)=vx*t
35=vx*2.12
vx=35/2.12
16.5 m/s

3) The time of flight is twice the time to apogee
vy(t)=12*sin(28)-9.8*t
apogee occurs when vy(t)=0
t=12*sin(28)/9.8
peak height is apogee
y(t)=12*sin(28)*t-.5*9.8*t^2
plug in t
peak height=.5*9.8*(12*sin(28))^2
horizontal distance is


flight time is 24*sin(28)/9.8
x(t)=12*cos(28)*t
plug in t for the flight time and solve
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