Chapter ISG, Problem 9.3.3P

a.

To determine

To calculate where does intersect x axis.

Answer to Problem 9.3.3P

The graph intersect at $t=0$ and $t=10$

Explanation of Solution

Given information:

Height of rocket

  $h=-16t^2+160t$

Calculation:

when $h=0$

Then,

  $0=-16t^2+160t$

On solving,

  $16t(t^{}-10)=0$

On solving,

  $16t=0$ and $(t^{}-10)=0$

On solving,

  $t=0$ and $t=10$

The graph intersect at $t=0$ and $t=10$

b.

To determine

To calculate how long after jumping did rocket to reach maximum height.

Answer to Problem 9.3.3P

At $t=5$ seconds rocket attain maximum height.

Explanation of Solution

Given information:

Height of rocket

  $h=-16t^2+160t$

Calculation:

  $h=-16t^2+160t$

Maximum height is 400

then, $h=400$

Substituting value of h

  $400=-16t^2+160t$

On solving,

  $16t^2-160t+400=0$

On solving,

  $t^2-10t+25=0$

On solving,

  $t=\frac{10\pm \sqrt{{10}^2-4(1)(25)}}{2(1)}$

On solving,

  $t=5$ seconds

At $t=5$ seconds rocket attain maximum height.