A penknife drops out of a sailor’s hand while she is at the top of a mast. She times the knife’s drop to the deck and measures 1.3 s. a) How high was she up the mast? b) With what speed did the knife hit the deck? c) What was the knife’s average speed?
Answer
Penknife Drop from Mast: Free Fall Physics Problem
In this scenario, a sailor drops a penknife from the top of a mast. She times the fall and notes it took 1.3 seconds to hit the deck. Let’s use the kinematic equations to find the required values step-by-step.
🔢 Given Data
Time of fall, t = 1.3 s
Initial velocity, u = 0 m/s (free fall from rest)
Acceleration due to gravity, g = 9.8 m/s²
🅐 How high was she up the mast?
Use the kinematic equation for displacement:
Since u = 0:
🅑 With what speed did the knife hit the deck?
Use the formula for final velocity in free fall:
Since u = 0:
🅒 What was the knife’s average speed?
Average speed is total displacement divided by time:
Note: In free fall from rest, average speed is also equal to half the final speed (v/2), which confirms this result.