### Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem6-74

6-74.

From her second floor window $6$ meters above the ground, Xiomara throws a tennis ball at a rate of $11$ meters per second up towards her friend Itzagueri who is $12$ meters above the ground. Assume $a(t) =-9.8$ meters per sec$^2$ for the acceleration due to gravity.

1. Assuming Itzagueri does not catch the ball, describe the motion of the ball $2$ seconds after it was thrown.

At $t = 2$, is the ball rising or falling? Is it's velocity increasing or decreasing?

2. When does the ball reach its highest point?

The ball stops moving at its highest point.

3. Will the ball reach Itzagueri? Support your answer with calculations.

The height is given by $h(t) =-4.9t^2 + 11t + 6$.
$h$(answer from part (b)) $≈ 12.173$ m; so yes.

4. Determine how high the ball is when it is falling at the rate of $5$ meters per second.

Before you evaluate the height, find the time when $v(t) =-5.$

5. Explain what $\int _ { 0 } ^ { 2 } a ( t ) d t$ represents physically.

Be sure to explain the significance of BOTH the integrand and the bounds.