Question

The height of a toy rocket shot upward can be found using the formula

h=−16t^2 +90t. The height of a rising balloon follows the formula h=10t. If they are released together, find the time it takes for the toy rocket and the balloon to reach the same height. Solve by graphing.
Options:
A. 1.5 seconds
B. 2 seconds
C. 2.5 seconds

Answer 1

The time it takes for the toy rocket and the balloon to reach the same height is 5 seconds.

Step-by-step explanation:

To find the time it takes for the toy rocket and the balloon to reach the same height, we need to set the two height equations equal to each other: -16t^2 + 90t = 10t. Rearranging the equation, we get 16t^2 - 80t = 0. Factoring out 16t, we have t(16t - 80) = 0. So t = 0 or t = 5. Since time cannot be negative, the time it takes for the toy rocket and the balloon to reach the same height is 5 seconds.