Question

A hockey puck slides across the ice with an initial velocity of 7.2 m/s. It has a deceleration of 1.1 m/s2 and is traveling toward the goal 5.0 m away. How much time does the goalie have to stop the puck​

Answer 1

Answer:

0.74 s

Explanation:

We can solve the problem by using the following SUVAT equation:

$d = ut + \frac{1}{2}at^2$

where

d = 5.0 m is the displacement

u = 7.2 m/s is the initial velocity

a = -1.1 m/s^2 is the acceleration (which is negative since it is a deceleration)

t is the time

Substituting numbers into the equation, we find:

$5.0 = 7.2 t -0.55t^2\\0.55t^2 -7.2t + 5.0 = 0$

This is a second-order equation, whose solutions are given by:

$t=\frac{-(-7.2) \pm \sqrt{(-7.2)^2-4(0.55)(5.0)}}{2(0.55)}$

And the solutions are

t = 0.74 s

t = 12.36 s

The solution we are looking for is the first one, because it corresponds to the first time at which the hockey puck has travelled the distance of 5.0 m, reaching the goal.