Question

A ball slips off a frictionless table at a speed of 7 m/s. The ball falls in a parabolic motion and hits 2.2 m along the ground. How high is the table off the ground? What is the magnitude of the angle of the ball with respect to the x-axis of the velocity of the ball just before it hits the ground?

Answer 1

We need to know how fast the ball is moving in the vertical direction to find an angle. We only know horizontal is 7 m/s. To find the height of the table, we need to know how long it was falling for. We're missing information.

We should find time first using the horizontal information given.

t = x / v = 2.2 / 7 = 0.314 s

Okay, so now we are set to find out how high the table is. We know how long the ball fell and the only force acting on it falling is gravity. So let's use the free-fall equation.

h = 0.5 * g * t^2 = (0.5) (9.8) (0.314)^2 = 0.483 m

Lastly, let's move on to speed just before hitting the ground. The final velocity (since the initial velocity is 0) is simply the amount the object accelerated multiplied by how long it was doing so.

Vf = Vi + a * t : in our case, Vi was 0 before it started falling

Vf = g * t = (9.8) (0.314) = 3.08 m/s

Now, we can use trigonometry to find an angle. We know that the horizontal velocity never changes for projectiles (no forces acting in horizontal direction). We just found the vertical velocity.

V(h) = 7 m/s
V(v) = 3.08 m/s

Draw a triangle and find the angle using the tangent function, since these are the adjacent and opposite sides:
This means:

angle (w.r.t x-axis) = tan^-1 (3.08 / 7) = 23.75 degrees