A Nile cruise ship takes 21.7 h to go upstream from Luxor to Aswan, a distance of 208 km, and 19.4 h to make the return trip downstream. Assuming the ship's speed relative to the water is the same in both cases, calculate the speed of the current in the Nile.
Calculate upstream rate = d/t.
Calculate downstream rate = d/t.
subtract rates to obtain speed of the river.
A motor scooter rounds a curve on the highway at a constant speed of 25.0 m/s. The original direction of the scooter was due east; after rounding the curve the scooter is heading 28 degrees north of east. The radius of curvature of the road at the location of the curve is 160 m.
What is the average acceleration of the scooter as it rounds the curve?
To calculate the speed of the current in the Nile, we first need to understand the relationship between the speed of the boat and the speed of the current.
Let's assume that the speed of the boat relative to the water is represented by 'v' and the speed of the current is represented by 'c'.
When the boat is traveling upstream, it moves against the current. Therefore, the effective speed of the boat is reduced by the speed of the current. So, the speed of the boat relative to the ground is (v - c). Similarly, when the boat is traveling downstream, it moves with the current, so the effective speed of the boat is increased. Thus, the speed of the boat relative to the ground is (v + c).
Now, we can use the formula: Distance = Speed × Time to calculate the speed of the current.
For the upstream journey: Distance = 208 km, Time = 21.7 hours, and Speed = (v - c).
Similarly, for the downstream journey: Distance = 208 km, Time = 19.4 hours, and Speed = (v + c).
Using these equations, we can set up two equations as follows:
208 = (v - c) × 21.7 (upstream journey)
208 = (v + c) × 19.4 (downstream journey)
Now, we can solve these two equations simultaneously to find the values of 'v' and 'c'.
Let's multiply the first equation by 19.4 and the second equation by 21.7 to eliminate the variables 'v' and 'c':
4043.6 = (v - c) × 19.4 × 21.7
4273.6 = (v + c) × 19.4 × 21.7
Subtracting the two equations, we get:
4273.6 - 4043.6 = 41.6vc
Simplifying:
230 = 41.6vc
Now, divide both sides of the equation by 41.6:
vc = 230 / 41.6
Therefore, the speed of the current in the Nile is approximately 5.53 km/h.