A stationary 1.67-kg object is struck by a stick. The object experiences a horizontal force given by F = at ‐ bt^2, where t is the time in seconds from the instant the stick first contacts the object. If a = 15 N/s and b =20 N/s^2, what is the impulse of the force over the period 0 s t = 3.0 s?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Alead ball is dropped into a lake from a diving board 5m above the water . it hits the water with a certain velocity and then sink with constant velocity in bottom . it reaches the bottom 5 second after it is dropped if g= 10m/s2 . find depth of the lake and average velocity of the ball ?

Need asap ‼️ 20 pts which gravitational force field diagram is drawn correctly? (answers in pictures below)