Question

On planet Mars, an astronaut jumps off a 2.00 m high boulder onto the ground. Her height above the ground in meters as a function of time in seconds is given by h(t)=−1.89t² + 2.34t + 2.00

• When, to the nearest hundredth of a second, will she land on the ground?

Answer 1

To find out when the astronaut lands on Mars, we set the height function h(t) = -1.89t² + 2.34t + 2.00 to zero and solve for t using the quadratic formula. Discarding the negative time, we determine the time to the nearest hundredth of a second when the astronaut's height is zero, indicating landing.

Step-by-step explanation:

To determine when the astronaut will land on Mars, we need to find when her height h(t) above the ground is 0. The function representing her height is given by h(t) = -1.89t² + 2.34t + 2.00. To find when the astronaut lands, set h(t) to zero and solve for t:

0 = -1.89t² + 2.34t + 2.00.

Using the quadratic formula, t = (-b ± √(b²-4ac)) / (2a), where a = -1.89, b = 2.34, and c = 2.00, we find two potential times for when the astronaut's height could be zero. However, we discard the negative time as it is not physically meaningful in this context. We are left with one time where the astronaut's height becomes zero, which is when she lands. Once calculated, this time to the nearest hundredth of a second will answer the student's question.