Question

A rugby player kicks a rugby ball 2 feet above the ground with an initial vertical velocity of 50 feet per second. The function h=−16t^2+50t+2 represents the height h (in feet) of the rugby ball after t seconds. Use a graphing calculator to estimate when the height of the rugby ball is 35 feet.

Answer 1

Step-by-step explanation:

It is given that,

A rugby player kicks a rugby ball 2 feet above the ground with an initial vertical velocity of 50 feet per second. The height h of the rugby ball after t second is given by :

$h=-16t^2+50t+2$ ......(1)

Here,

h is height in feet and t is in seconds

We need to find the time when the height of the ball is 35 feet. For this equation (1) will becomes :

$35=-16t^2+50t+2\\\\-16t^2+50t+2-35=0\\\\-16t^2+50t-33=0$

We can plot the graph of the above equation using Desmos calculator. The attached figure shows the time when the height of the rugby ball is 35 feet.

It is clear form the graph that the ball with have height of 35 feets at t = 0.947 s and 2.178 s.