Question

Josh hit a baseball straight up into the air. The equation below describes the height of the ball, h, as a function of time, t. What is the height of the ball after 3 seconds?

h(t) = -9.81t^2 + 30t + 1.5
a) 3.3 meters
b) 62.1 meters
c) 120.9 meters
d) 179.7 meters

Answer 1

To find the height of the ball after 3 seconds, we substitute t = 3 into h(t) = -9.81t^2 + 30t + 1.5. The calculation yields a height of approximately 3.21 meters, which would be closest to option (a) if rounded to 3.3 meters.

Step-by-step explanation:

To determine the height of the ball after 3 seconds, we need to substitute the value of t = 3 seconds into the given quadratic equation h(t) = -9.81t^2 + 30t + 1.5. This will give us the height of the baseball at that specific time.

By plugging in the value, we get:

1. h(3) = -9.81(3)^2 + 30(3) + 1.5
2. h(3) = -9.81(9) + 90 + 1.5
3. h(3) = -88.29 + 90 + 1.5
4. h(3) = 3.21 meters

The calculated height does not exactly match any of the provided options, indicating there might be a rounding difference or miscalculation in the question. If we assume the question intended for the calculation to yield one of the provided answers, the closest match by rounding would be 3.3 meters, which is option (a). However, it's essential to double-check the calculation and the given options for any discrepancies.