Aball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft. approximentaly how long does is take for the ball to hit the ground. acceleration due to gravity is 32ft/s^2

The ball takes 2.47 seconds to touch the ground

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is:

Where is the initial height, is the initial velocity and t is the time in seconds.

We know that the initial height is:

The initial speed is:

So the equation is:

The ball hits the ground when when

So

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

The quadratic formula is:

In this case

Therefore

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground