Find the time required for the boat to slow to 45 km/hr

[king_naeem]

hey

A 1000 kg boat is traveling at 90km/h when its engine is shut off. The magnitude of the frictional force between boat and water is proportional to the speed v of the boat: force of kinetic fricition=70v, where v is in meters per second and the force is in Newtons. Find the time required for the boat to slow to 45 km/hr

 

[dextercioby]

hey

A 1000 kg boat is traveling at 90km/h when its engine is shut off. The magnitude of the frictional force between boat and water is proportional to the speed v of the boat: force of kinetic fricition=70v, where v is in meters per second and the force is in Newtons. Find the time required for the boat to slow to 45 km/hr

I'm a theorist,so i'll let u plug the numbers:
The Newton's law states:m\frac{dv}{dt}=-\alpha v,where alpha is that 70 in your problem:
Integrate the ODE wrt to proper limits:
Final result:t=(\frac{1000}{70}\ln 2) s

Good luck!

 

[wais]

.

To find the time required for the boat to slow to 45 km/hr, we can use the formula for acceleration: a = F/m, where a is the acceleration, F is the net force, and m is the mass of the boat. In this case, the net force is the frictional force, which is given by 70v. We can also convert the speed of the boat from km/hr to m/s by multiplying it by 1000/3600 (since 1 km/hr = 1000/3600 m/s). So, the speed of the boat in m/s is 45 * 1000/3600 = 12.5 m/s.

Now, we can plug in the values into the formula for acceleration:

a = 70 * 12.5 / 1000 = 0.875 m/s^2

Next, we can use the formula for uniform acceleration to find the time required for the boat to slow down from 12.5 m/s to 0 m/s:

v = u + at

Where v is the final velocity (0 m/s), u is the initial velocity (12.5 m/s), a is the acceleration (0.875 m/s^2) and t is the time we are looking for. Rearranging the equation to solve for t, we get:

t = (v-u)/a = (0 - 12.5)/0.875 = -14.29 seconds

However, we cannot have a negative time, so we can conclude that it will take approximately 14.29 seconds for the boat to slow down from 90 km/hr to 45 km/hr.