Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. what is the speed of the train, if it is 5 km/h gre
1 answer:
The distance covered by car is equal to (assuming it is moving by uniform motion) the product between the car's speed and the time of the car ride, 4 h:
where
is the car's speed
is the duration of the car ride
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
which becomes
(1)
we also know that the train speed is 5 km/h greater than the car's speed:
(2)
If we put (2) into (1), we find
and if we solve it, we find
So, the car speed is 20 km/h and the train speed is 25 km/h.
where
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
which becomes
we also know that the train speed is 5 km/h greater than the car's speed:
If we put (2) into (1), we find
and if we solve it, we find
So, the car speed is 20 km/h and the train speed is 25 km/h.
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(a) +2.60 m/s
The motion of the fish dropped by the seagul is a projectile motion, which consists of two independent motions:
- a horizontal uniform motion, at constant speed
- a vertical motion, at constant acceleration (acceleration of gravity, , downward)
In this part we are only interested in the horizontal motion. As we said the horizontal component of the fish's velocity does not change, therefore its value when the fish reaches the ocean is equal to its initial value, which is the speed at which the seagull was flying (because it was flying horizontally):
(b) -17.2 m/s
The vertical component of the fish's velocity instead follows the equation:
where
is the initial vertical velocity, which is zero
is the acceleration of gravity
t is the time
Since the fish reaches the ocean at t = 1.75 s, we can substitute this time into the formula to find the final vertical velocity:
where the negative sign indicates the direction (downward).
(c)
The horizontal component of the fish's velocity would increase
The vertical component of the fish's velocity would stay the same.
As we said from part (a) and (b):
- The horizontal component of the fish's velocity is constant during the motion and it is equal to the initial velocity of the seagull -> so if the seagull's initial speed increases, the horizontal velocity of the fish will increase too
- The vertical component of the fish's velocity does not depend on the original speed of the seagull, therefore it is not affected.