(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A hockey player is standing on his skates on a frozen pond when an opposing

player skates by with the puck, moving with a constant speed of 12 m/s. After

3.0 s, the first player makes up his mind to chase his opponent and starts

accelerating uniformly at 3.8 m/s^2.

(a) How long does it take him to catch his opponent?

(b) How far does he travel before he catches up with his opponent?

2. Relevant equations

3. The attempt at a solution

We know the initial velocities and accelerations of the two players,

a1 = 4 m/s2, a2 = 0

v1i = 0, v2i = 12 m/s

x1i = x2i = 0

The position of player #2 is given by

x2 = x2i + v2i t + (1/2) a2 t2

x2 = (12 m/s) t

Be careful with the time. We must account for player #1's wait of 3 s. With this accounted for, we can calculate the position of player #1 from

x1 = x1i + v1i (t - 3 s) + (1/2) a1 (t - 3 s)2

Of course, this equation only makes sense for t > 3 s.

x1 = 0 + 0 + (1/2) (3.8 m/s2) (t - 3 s)2 = (2 m/s2) (t2 - 6 s t + 9 s2)

Now we set x1 = x2 and solve for the time t.

x1 = x2

(1.9 m/s2) (t2 - 6 s t + 9 s2) = (12 m/s) t

We can either keep the units in explicitly or ensure that we have consistent units and simply write

1.9 (t2 - 6t + 9) = 12t

1.9 t2 - 12 t + 18 = 12 t

1.9 t2 - 24 t + 18 = 0

There are two solutions to this quadratic equation,

t1 = 11.8 s, and t2 = 0.8 s

However, the equation for the position of player #1 is not valid for t2 < 3 s, so we keep only tx,

t = 11.8 s

(b) How far has the first player traveled in this time?

Now where is player #2 (and, therefore, player #1 as well) at this time?

x2 = x2i + v2i t + (1/2) a2 t2

x2 = (12 m/s) t

x2 = (12 m/s) (11.8 s)

x2 = 141.6 m

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Please check my acceleration hockey answer.

**Physics Forums | Science Articles, Homework Help, Discussion**