A pigeon flying horizontally at a speed of 16.0 m/s drops a stolen Rolex watch. The timepiece falls to the ground in 2.90s. (a) What was the watsh's altitude when it was dropped? (b) how far horizontally did it travel before it smashed into the deck?
To find the answers to both parts of the question, we can use the equations of motion. Let's break down the problem step by step.
(a) What was the watch's altitude when it was dropped?
We know that the watch falls for a time of 2.90 seconds. The acceleration due to gravity is approximately 9.81 m/s².
Using the equation of motion for vertical motion:
Δy = viy * t + (1/2) * a * t²
where:
Δy is the change in vertical position (altitude),
viy is the initial vertical velocity (which is zero since the watch was dropped),
a is the acceleration due to gravity,
t is the time.
Plugging in the values we know:
Δy = 0 + (1/2) * 9.81 * (2.90)²
Δy = 42.165 m
Therefore, the watch's altitude when it was dropped was 42.165 meters.
(b) How far horizontally did it travel before it smashed into the deck?
Since the pigeon is flying horizontally at a constant speed, there is no acceleration in the horizontal direction.
The horizontal distance traveled can be calculated using the equation:
d = vix * t
where:
d is the horizontal distance traveled,
vix is the initial horizontal velocity (which is the same as the pigeon's velocity, 16.0 m/s),
t is the time.
Plugging in the values we know:
d = 16.0 * 2.90
d = 46.4 m
Therefore, the watch traveled 46.4 meters horizontally before it smashed into the deck.
To solve this problem, we can use the equations of motion to find the altitude and horizontal distance traveled by the watch.
(a) To find the altitude when the watch was dropped, we can use the equation:
h = vt + (1/2)gt^2
where:
h = altitude
v = initial velocity in the y-direction (vertical direction)
t = time
g = acceleration due to gravity (-9.8 m/s^2)
Given:
v = 0 (since the watch was dropped, not thrown)
t = 2.90 s
Plugging in the values, the equation becomes:
h = 0 + (1/2)(-9.8)(2.90)^2
Calculating this, we find:
h ≈ -40.19 m
The negative sign indicates that the altitude is below the point of reference.
Therefore, the watch's altitude when it was dropped is approximately -40.19 meters.
(b) To find the horizontal distance traveled by the watch before it smashed into the deck, we can use the equation:
d = vt
where:
d = horizontal distance
v = velocity in the x-direction (horizontal direction)
t = time
Given:
v = 16.0 m/s
t = 2.90 s
Plugging in the values, the equation becomes:
d = 16.0 * 2.90
Calculating this, we find:
d ≈ 46.40 m
Therefore, the watch traveled approximately 46.40 meters horizontally before it smashed into the deck.