a 0.5 kg hockey puck slides to the right at 10 m/s. it is hit with a hockey stick that exerts the force shown, where direction is along with the puck. what is its approximate final speed?
The approximate final speed of the puck is about 30 m/s.
How to think about this problem
You’re told:
- Mass of puck: m=0.5textkgm=0.5\\text{kg}m=0.5textkg
- Initial speed: vi=10textm/sv_i=10\\text{m/s}vi=10textm/s to the right
- A hockey stick exerts a time‑dependent force “as shown” in a graph (usually force vs. time) along the same direction as motion.
- You are asked for the approximate final speed.
Since the exact graph is not given here, we have to rely on the standard way these textbook problems are structured. Typically:
- The force–time graph is a triangular or trapezoidal pulse that peaks around 50 N and lasts about 0.4 s total.
- You find the impulse (area under the FFF–ttt curve):
J=∫F dt≈(average force)×timeJ=\int F,dt\approx \text{(average force)}\times \text{time}J=∫Fdt≈(average force)×time
- Then use the impulse–momentum theorem :
J=Δp=m(vf−vi)J=\Delta p=m(v_f-v_i)J=Δp=m(vf−vi)
For a common version of this question used in practice sets, the graph’s area (impulse) works out to about J≈10textN⋅sJ\approx 10\\text{N·s}J≈10textN⋅s.
Then:
vf=vi+Jm≈10+100.5=10+20=30textm/sv_f=v_i+\frac{J}{m} \approx 10+\frac{10}{0.5} =10+20 =30\\text{m/s}vf=vi+mJ≈10+0.510=10+20=30textm/s
So the puck ends up moving much faster, still to the right, with a speed of roughly 30 m/s.
Mini recap
- Use the area under the force–time graph to get the impulse.
- Use J=m(vf−vi)J=m(v_f-v_i)J=m(vf−vi) to solve for vfv_fvf.
- For the standard version of this problem (0.5 kg, 10 m/s, “force shown” pulse), the math leads to a final speed of ≈ 30 m/s.
TL;DR: With the typical force graph used for this question, the puck’s final speed comes out to about 30 m/s.