Question

Natalie found a tennis ball outside of a tennis court. She picked up the ball and threw it over the fence into the court. The path of the ball can be represented by the equation h= -5t²+10t+2 How long will it take to reach the ground? Round your answer to the nearest tenth of a second.

a) 2.4 seconds
b) 2.8 seconds
c) 3.2 seconds
d) 3.6 seconds

Answer 1

To find the time for the tennis ball to reach the ground, the quadratic equation -5t² + 10t + 2 = 0 is solved. The positive value after applying the quadratic formula is 2.4 seconds, rounded to the nearest tenth, which is the correct time for the ball to hit the ground.

Step-by-step explanation:

The equation h = -5t² + 10t + 2 represents the height of the tennis ball over time. To find how long it will take to reach the ground, you need to determine when the height h is equal to 0. This is because the ground is where the height is 0. So, we need to solve the quadratic equation -5t² + 10t + 2 = 0. By applying the quadratic formula, we get two possible times, but we take the positive value since time can't be negative. The quadratic formula yields two solutions but only the positive value makes physical sense in this context as it represents the time after the ball has been thrown. Rounding to the nearest tenth, the correct time for the ball to reach the ground is approximately 2.4 seconds, which is answer option (a).