A Dodge Stealth is driving at 70 mph on a highway. It passes a BMW going the same direction. The BMW is moving 7 mph backward relative the Dodge. What is the velocity of the BMW? Let the positive direction be forward.
-63 mph
-77 mph
77 mph
63 mph
A helicopter above the ground is descending at 3.1 m/s. It drops a package from rest(relative to the helicopter). Just before it hits the ground the package is falling at a rate of 9.5 m/s relative to the helicopter. Find the velocity of the package relative to the ground.
12.6 m/s, Up
6.4 m/s, Up
12.6 m/s, down
6.4 m/s, down
PLEASE EXPALIN HOW TO GET THE ANSWER AND THE CORRECT ANSWER. Thanks!
What was the answer to these?
Question 1:
To find the velocity of the BMW relative to the ground, we need to add the velocities of the Dodge and the BMW relative to each other. Since the BMW is moving 7 mph backward relative to the Dodge, we can subtract 7 mph from the Dodge's velocity.
The Dodge is moving at 70 mph and the BMW is moving 7 mph backward, so the velocity of the BMW relative to the ground would be 70 mph - 7 mph = 63 mph.
Therefore, the correct answer is 63 mph.
Question 2:
To find the velocity of the package relative to the ground, we can subtract the velocity of the helicopter from the velocity of the package relative to the helicopter.
The helicopter is descending at a velocity of 3.1 m/s, and just before it hits the ground, the package is falling at a velocity of 9.5 m/s relative to the helicopter.
Since the package is "dropped from rest", we can say that its initial velocity relative to the helicopter is 0 m/s.
To find the velocity relative to the ground, we subtract the velocity of the helicopter from the velocity of the package relative to the helicopter:
Velocity of package relative to the ground = Velocity of package relative to the helicopter - Velocity of helicopter
Velocity of package relative to the ground = 9.5 m/s - 3.1 m/s = 6.4 m/s, down
Therefore, the correct answer is 6.4 m/s, down.
To find the velocity of the BMW in the first question, we need to consider the relative velocities. The Dodge is driving at 70 mph and the BMW is moving 7 mph backwards relative to the Dodge. So, we need to subtract the velocity of the BMW from the velocity of the Dodge to get the relative velocity of the BMW.
Velocity of the BMW = Velocity of the Dodge - Relative velocity of the BMW
Velocity of the BMW = 70 mph - (-7 mph) (since the BMW is going backwards)
Velocity of the BMW = 70 mph + 7 mph
Velocity of the BMW = 77 mph
Therefore, the correct answer is 77 mph.
Now let's move on to the second question. We need to find the velocity of the package relative to the ground.
The package is dropped from rest relative to the helicopter, which means its initial velocity is 0 m/s relative to the helicopter. Just before it hits the ground, the rate at which it is falling relative to the helicopter is 9.5 m/s downwards.
To find the total velocity of the package relative to the ground, we need to consider the descending velocity of the helicopter. The helicopter is descending at 3.1 m/s. Since the package is also dropping down, we need to subtract the descending velocity of the helicopter from the falling rate of the package relative to the helicopter.
Velocity of the package relative to the ground = Falling rate of the package relative to the helicopter - Descending velocity of the helicopter
Velocity of the package relative to the ground = 9.5 m/s - (-3.1 m/s) (since the helicopter is descending downwards)
Velocity of the package relative to the ground = 9.5 m/s + 3.1 m/s
Velocity of the package relative to the ground = 12.6 m/s
Therefore, the correct answer is 12.6 m/s, downwards.