Solve the given problem

Question

A tennis ball rolls off the edge of a table top 1.00 m above the floor and strikes the floor at a point 2.60 m horizontally from the edge of the table. Find the time of the flight. Find the magnitude of the initial velocity. Find the magnitude the ball's velocity just before it strikes the floor. Find the direction of the ball's velocity just before it strikes the floor.

Answer 1

Time of flight is dictated by how long the ball remains in the air before touching the ground. This means the time of flight is only affected by forces in the y-direction, i.e. gravity. Since we are solving for time and the ball's initial y-velocity is 0, we know we need an equation with time, acceleration, initial velocity, and distance. Looking at our kinematic equations we can find:

Δx = v₀t + .5at²

Which give us a time of t = .45s for our time of flight. Using this, we can find the initial velocity by dividing the horizontal distance by time of flight.

2.6/.45 = v₀ = 5.78m/s

The x-component of the velocity will remain constant since there are no forces affecting it, which means the final x-component velocity is equal to the initial. To find the y-component we can use another kinematic equation:

v = v₀ + at = 9.81 * .45 = 4.41m/s

We can then use the components to form a triangle and calculate the magnitude of the final velocity using Pythagorean theorem.

(4.41)² + (5.78)² = v²

We can also take the inverse tangent of the components to find the angle of the final velocity.

tan^-1(4.41/5.78) = θ