Physics question about a tennis ball's velocity ?
a tennis ball rolls off the edge of a table top 0.750m above the floor and strikes the floor at a point 1.40m horizontally form the edge of the table top. ignore air resistance.
a) find the time of flight
b) find the magnitude of the initial velocity
c) find the magnitude and direction of the velocity of the ball just before it strikes the floor
a. The ball simply falls a distance 0.75 m.
s = (1/2)gt^2
s = 0.75m
g = 9.8 m/s^2
0.75 = (1/2)(9.8)t^2
t = SQRT[1.5/9.8] = SQRT[0.15306]
t = 0.391 seconds
b. The ball rolls off the table so it only has a horizontal velocity component as it leaves the table. It then hits the floor 1.4 meters from the table edge. It does this 0.391 seconds after leaving the table.
speed = distance/time = 1.4/0.391
speed =3.578 m/s
c. The horizontal component we just found in part (b). We just need to find the vertical component and this is due to gravity.
v = g*t = 9.8(0.391) = 3.834 m/s
magnitude = SQRT[(3.834)^2 + (3.578)^2]
magnitude = SQRT[27.502]
magnitude = 5.244 m/s
The direction relative to the floor will be:
tan(Angle) = (vertical component)/(horizontal component)
tan(Angle) = 3.578/3.834 = 0.93321
Angle = 43.021 degrees
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