A police car traveling at 94.5 km/h is traveling west, chasing a motorist traveling at 77.2 km/h.
(a) What is the velocity of the motorist relative to the police car?
The magnitude and its direction
(b) What is the velocity of the police car relative to the motorist?
The magnitude and its direction
(c) If they are originally 250 m apart, in what time interval will the police car overtake the motorist?
A full working would be appreciated! thanks!
Sure thing! Let's break it down step by step:
(a) To find the velocity of the motorist relative to the police car, we need to subtract the velocity of the police car from the velocity of the motorist.
The velocity of the motorist is 77.2 km/h towards the west (-77.2 km/h).
The velocity of the police car is 94.5 km/h towards the west (-94.5 km/h).
So, the velocity of the motorist relative to the police car is 77.2 km/h - (-94.5 km/h), which simplifies to 171.7 km/h towards the west.
(b) To find the velocity of the police car relative to the motorist, we apply the same logic.
The velocity of the motorist is 77.2 km/h towards the west (-77.2 km/h).
The velocity of the police car is 94.5 km/h towards the west (-94.5 km/h).
So, the velocity of the police car relative to the motorist is -94.5 km/h - (-77.2 km/h), which simplifies to -17.3 km/h towards the west.
Note: The negative sign indicates that the police car is behind the motorist.
(c) To find the time interval it takes for the police car to overtake the motorist, we can use the relative velocity.
The initial separation between them is 250 m.
Relative velocity = 171.7 km/h = (171.7 km/h * 1000 m/km) / (3600 s/h) = 47.7 m/s (approx.)
To overtake the motorist, the police car needs to close the initial separation of 250 m.
Time = Distance / Relative velocity = 250 m / 47.7 m/s = 5.24 seconds (approx.)
So, the police car will overtake the motorist in approximately 5.24 seconds.
I hope this helps! If you have any more questions or need further assistance, feel free to ask!
To solve this problem, we'll need to understand how to calculate relative velocities. The relative velocity is the velocity of an object with respect to another object.
(a) To find the velocity of the motorist relative to the police car, we need to subtract the velocity of the police car from the velocity of the motorist. Since the police car is traveling west, its velocity will have a negative sign.
Relative velocity = Velocity of the motorist - Velocity of the police car
Relative velocity = 77.2 km/h - (-94.5 km/h) [Note: subtracting a negative is the same as adding]
Relative velocity = 77.2 km/h + 94.5 km/h
Relative velocity = 171.7 km/h
Therefore, the velocity of the motorist relative to the police car is 171.7 km/h west.
(b) To find the velocity of the police car relative to the motorist, we need to subtract the velocity of the motorist from the velocity of the police car. Since the motorist is traveling west, its velocity will have a negative sign.
Relative velocity = Velocity of the police car - Velocity of the motorist
Relative velocity = -94.5 km/h - 77.2 km/h
Relative velocity = -171.7 km/h
Therefore, the velocity of the police car relative to the motorist is 171.7 km/h east.
(c) To find the time interval for the police car to overtake the motorist, we need to calculate the distance traveled by each object.
Let's assume the time taken by the police car to overtake the motorist is 't' seconds.
Distance traveled by the police car = 94.5 km/h * t
Distance traveled by the motorist = 77.2 km/h * t
Since they are initially 250 m apart, we can set up the following equation:
Distance traveled by the police car - Distance traveled by the motorist = 250 m
(94.5 km/h * t) - (77.2 km/h * t) = 250 m
17.3 km/h * t = 250 m
Converting km/h to m/s, we have:
17.3 km/h * (1000 m/km) * (1/3600 h/s) * t = 250 m
0.0048 m/s * t = 250 m
t = 250 m / 0.0048 m/s
t ≈ 52,083.33 s
Therefore, it will take approximately 52,083.33 seconds for the police car to overtake the motorist.
To solve this problem, we'll use the concepts of relative velocity and time-distance calculations.
(a) To determine the velocity of the motorist relative to the police car, we can subtract the velocity of the police car from the velocity of the motorist.
Relative velocity = Velocity of motorist - Velocity of police car
Given:
Velocity of motorist = 77.2 km/h
Velocity of police car = 94.5 km/h (assuming west is positive)
Substituting the values:
Relative velocity = 77.2 km/h - 94.5 km/h
Relative velocity = -17.3 km/h
The magnitude of the relative velocity is 17.3 km/h, and its direction is opposite to the direction of the police car (east).
(b) To determine the velocity of the police car relative to the motorist, we again subtract the velocity of the motorist from the velocity of the police car.
Relative velocity = Velocity of police car - Velocity of motorist
Relative velocity = 94.5 km/h - 77.2 km/h
Relative velocity = 17.3 km/h
The magnitude of the relative velocity is 17.3 km/h, and its direction is the same as the direction of the police car (west).
(c) To find the time interval when the police car overtakes the motorist, we need to determine the distance covered by both vehicles.
Initially, the distance between the vehicles is given as 250 m (0.25 km). The police car will keep chasing the motorist until they cover the same distance.
Let's set up an equation to find the time:
Distance covered by police car = Distance covered by motorist
Velocity of police car * Time taken by police car = Velocity of motorist * Time taken by motorist
(94.5 km/h) * t = (77.2 km/h) * t
Simplifying the equation:
94.5t = 77.2t
Rearranging the equation:
94.5t - 77.2t = 0
17.3t = 0
t = 0
The time interval is t = 0, which means the police car overtakes the motorist instantaneously.
Hence, the police car catches up with the motorist immediately.
a. Vm = 77.2 - 94.5 = -17.3 km/h.
b. Vp=94.5 - 77.2=17.3 km/h=Velocity of policeman.
c. Vm*t=X km=Dist traveled bymotorist.
Eq1: 77.2t = X.
Vp*t = (X+250)=Dist. traveled by police.
Eq2: 94.5t = X+0.250)km.
In Eq2, substitute 77.2t for x:
94.5t = 77.2t + 0.2525
94.5t - 77.2t = 0.25
17.3t = 0.25
t = 0.01453 h. = 0.87 min = 52.3 s.