Jack, jill and spot go out for a picnic at the side of the river. jack takes spot for a jog. jack and spot are on the wast bank of the 30m wide river when jill is on the east side. the rivers current is 0.75m/s south.
a) spot jumps into the river and swims straight east at 1.8m/s relitive to the water. once across spot runs 4m/s on the shore to get to jill. How long does to take spot to get to jill?
b)jack dives in the river and aims slightly upstream and swims 2m/s relitive to the water to go straight across. How many seconds does jack beat spot by?
a) time for spot to cross river: 30/1.8
spot goes this distance downstream*.75*30/1.8
time for spot to reach jil:30/1.8+distancdownstream/4
b> Jack swims at arctan .75/2 upstream. His velocity across the river is 2*cosine of that angle, and time across is 30/vacrossriver.
Do some calculating, and you have it.
thanks
To find the answers to these questions, we need to use the concept of relative velocities and the laws of motion.
a) To determine how long it takes for Spot to get to Jill, we need to find the time it takes for Spot to cross the river and the time it takes for Spot to run along the shore to reach Jill.
First, let's calculate the time it takes for Spot to cross the river. The width of the river is 30m, and Spot swims east at a speed of 1.8m/s relative to the water. However, we need to account for the river's current, which is flowing south at a speed of 0.75m/s.
To calculate the time it takes for Spot to cross the river, we divide the width of the river by the relative velocity of Spot to the water:
Time to cross the river = Width of river / Relative velocity
Relative velocity of Spot to the water = Spot's swimming speed - River's current speed
Relative velocity = 1.8m/s - 0.75m/s = 1.05m/s
Time to cross the river = 30m / 1.05m/s ≈ 28.57 seconds
Now, to calculate the time it takes for Spot to run along the shore to reach Jill, we divide the distance between Jill and the river bank by Spot's running speed:
Time to run along the shore = Distance along the shore / Spot's running speed
Since the distance Spot needs to run along the shore is not mentioned, we cannot calculate this time. The information provided is insufficient to compute the total time it takes for Spot to get to Jill.
b) To determine the number of seconds Jack beats Spot by, we need to calculate the time it takes for Jack to cross the river and compare it to the total time it takes for Spot to reach Jill.
Jack swims across the river aiming slightly upstream at a speed of 2m/s relative to the water. Again, we need to account for the river's current, which is flowing south at a speed of 0.75m/s.
To calculate the time it takes for Jack to cross the river, we divide the width of the river by the relative velocity of Jack to the water:
Time to cross the river = Width of river / Relative velocity
Relative velocity of Jack to the water = Jack's swimming speed - River's current speed
Relative velocity = 2m/s - 0.75m/s = 1.25m/s
Time to cross the river = 30m / 1.25m/s = 24 seconds
Therefore, Jack beats Spot by 28.57 - 24 = approximately 4.57 seconds.
Note: The calculations provided here assume that there are no other factors affecting the swimmer's motion, such as the angle of their swimming path.