A boat heads north at 30 mph while a steamer heads east at 40 mph at the same time. When is the distance between them 50 mi? Ans
1 answer:
Answer:
1 hour
Explanation:
Speed of the first boat = 30 mph
Speed of the second = 40 mph
The boats will cover different distances but the time taken will be the same.
Time taken by the boats = t
Distance = Speed × Time
Distance covered by the first boat = 30t
Distance covered by the second boat = 40t
Distance between the boats = 50 mi
From the Pythagoras theorem
Time taken by the boats when they are 50 mi away is 1 hour
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Answer:
The box stops in 0.139 seconds, after moving 7.29cm (0.0729m) backwards relative to the belt.
Explanation:
As the box is initially at rest relative to the earth, it is moving backwards with a speed of 1.05m/s relative to the belt. Then, the frictional force acts on the box to make it stop relative to the belt. So, we first have to write the equations of motion of the box in each axis:
Since the frictional force is equal to
, then we have that the acceleration is:
Now, from the definition of acceleration we get:
And, as the final velocity is zero because the box gets to a stop, we have:
(Don't worry about the negative sign. It will disappear because the initial velocity is also negative, since we take the box initially moving backwards)
Then, plugging in the given values, we calculate the time:
In words, the time the box takes to stop sliding relative to the belt is 0.139s.
The displacement of the box in this time, is given by the kinematics formula:
Finally, we calculate the displacement:
This means that the box moves 7.29cm backwards relative to the belt.