Question

a A circus juggler on a high wire tosses a juggling pin upward with an initial vertical velocity of 24 feet per second from a height of 37 feet. Part 1 out of 2 How long does it take the pin to reach its maximum height ? What is that height? The pin reaches its maximum height of _____feet _____second (s) after it is released.

Answer 1

Answer:

The pin reaches its maximum height of $66.39$  feet  $1.014$ second (s) after it is released

Step-by-step explanation:

Generally from kinematic equation

    $v^2 = u^2 + 2as$

Here v is 0 m/s given that the velocity at maximum height is zero

        s is the distance from the 37 feet to maximum height

        a is the acceleration due to gravity i.e (-9.8m/s^2 ) the negative sign shows that it is moving against gravity

So

         $0 = 24^2 + 2*( -9.8) * s$

=>       $s = 29.39 \ ft$

Generally the maximum height attained is  

      $H = 37 + 29.39$

     $H = 66.39 \ ft$

Generally from the  kinematic equation

      $s = ut + \frac{1}{2}(g)t^2$

=>   $29.39 = 24 t + 0.5 * 9.8 t^2$

=>  $29.39 = 24 t + 4.9 t^2$

=>   $4.9t^2 + 24 t -29.39$

Using quadratic formula to solve this equation we have

    $t = 1.014 \ s$