A pellet is fired through two circular plates .8 m apart, both rotating at -95rad/s. The angular displacement of second bullet hole is 82° from the first bullet hole. Calculate the bullet’s speed in m/s.
If someone could help me see where to insert the factors in whichever equation that would be very helpful. I'm stuck!
The second plate traveled 82deg
displacement=speed*time
82deg*PIrad/180deg=95rad/sec*time
time= 82*PI/180 / 95=.0150 sec
speed bullet= distance/time=.8m/.0150=53.3m/s
To solve this problem, we can first calculate the angular displacement of the second bullet hole, and then use this information to find the speed of the bullet.
Step 1: Calculate the angular displacement of the second bullet hole:
Given:
Angular velocity of both plates = -95 rad/s
Distance between the plates = 0.8 m
Angular displacement of the second bullet hole = 82°
To find the angular displacement of the second bullet hole, we can use the formula:
θ = ω * t
where θ is the angular displacement, ω is the angular velocity, and t is the time.
Since the angular velocity (ω) is the same for both plates, we can set up the equation:
θ = ω * t
Where:
ω = -95 rad/s (angular velocity)
θ = 82° (angular displacement in degrees)
To convert degrees to radians, we use the conversion factor:
1° = π/180 radians
So, θ = 82° * (π/180) = 82π/180 radians
Now, we can plug in the values into the equation and solve for t:
82π/180 = -95 * t
Step 2: Solve for t:
Dividing both sides of the equation by -95:
t = (82π/180) / -95
t ≈ -0.297 seconds (rounded to 3 decimal places)
Step 3: Calculate the bullet's speed:
To find the bullet's speed, we can use the formula:
v = d / t
where v is the velocity (speed), d is the distance, and t is the time.
Given:
Distance between the plates = 0.8 m
Time (t) = -0.297 seconds (negative sign denotes the direction of rotation)
Since the bullet travels from the first bullet hole to the second bullet hole, the distance traveled is the distance between the plates, which is 0.8 m:
v = 0.8 / -0.297
v ≈ -2.693 m/s (rounded to 3 decimal places)
The bullet's speed is approximately 2.693 m/s.