You and a friend are riding your bikes to a restaurant that you think is east and that your friend thinks is north. you both leave from the same starting point, with you riding 16 miles per hour east and your friend riding 12 miles per hour north. after you travel 4 miles, at what rate is the distance between you changing?

20 miles per hour

Explanation:

Let the east direction is denoted by x and the north direction is denoted by y.

so, dx / dt = 16 miles per hour

dy / dt = 12 miles per hour

x = 4 miles

Let the distance between both the friends be s.

Time taken by you to travel 4 mile, t = distance / speed = 4 / 12 = 1/4 hour

Distance traveled by your friend in time t, y = speed x time = 12 x 1/4 = 3 miles

Use Pythagorean theorem,

x^2 + y^2 + s^2     (1)

Substitute, x = 4 mile, y = 3 mile

s^2 = 16 + 9 = 25

s = 5 miles

Differentiate equation (1) with respect to t, we get

2x dx/dt + 2y dy/dt = 2s ds/dt

4 (16) + 3 (12) = 5 ds/dt

ds/dt = 20 miles per hour

Thus, the distance between you and your friend is changing with a rate of 20 miles per hour.

need to see circuit to get time constant

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards