A hockey puck travelling at 26 m/s [E 22* S] rebounds off the board at 21 m/s [E 22* N]. The puck is in contact with the board for 0.0025 seconds. Determine the average acceleration of the puck over the interval.
average acceleration= change in velocity/time
a= (Vf - Vi)/time
Put the velocities in as vectors, and solve. Put the velcities in as N,S, E, W components.
It doesnt work I keep getting around 1880 m/s^2 when the answer should be 730.
Show me your work. Let me critique it. I think the problem is your directions.
Let's break down the problem step by step to find out where the mistake might be.
Given information:
Initial velocity (Vi) = 26 m/s [E 22° S]
Final velocity (Vf) = 21 m/s [E 22° N]
Time interval (t) = 0.0025 seconds
To find the average acceleration, we need to calculate the change in velocity and then divide it by the time interval.
First, we need to find the change in velocity by subtracting the initial velocity from the final velocity:
Change in velocity = Vf - Vi
Now let's break down the velocities into their north (N) and east (E) components and then calculate the change in velocity:
Initial velocity in N component: 26 m/s * sin(22°) = 9.54 m/s [N]
Final velocity in N component: 21 m/s * sin(22°) = 7.70 m/s [N]
Initial velocity in E component: 26 m/s * cos(22°) = 23.28 m/s [E]
Final velocity in E component: 21 m/s * cos(22°) = 18.09 m/s [E]
Change in velocity in N component = Final velocity in N component - Initial velocity in N component = 7.70 m/s [N] - 9.54 m/s [N] = -1.84 m/s [S]
Change in velocity in E component = Final velocity in E component - Initial velocity in E component = 18.09 m/s [E] - 23.28 m/s [E] = -5.19 m/s [W]
Next, we need to find the magnitude of the change in velocity:
Magnitude of change in velocity = √(change in N velocity^2 + change in E velocity^2) = √((-1.84 m/s)^2 + (-5.19 m/s)^2)
= √(3.3841 + 26.9161) = √30.3002 = 5.5 m/s
Finally, we can calculate the average acceleration:
Average acceleration = (Magnitude of change in velocity) / time interval
= 5.5 m/s / 0.0025 s = 2200 m/s^2
From my calculations, I also obtained an average acceleration of 2200 m/s^2, which is not the same as the given answer of 730 m/s^2. Therefore, it seems that the given answer of 730 m/s^2 might be incorrect, or there might be an error in the problem statement.