An inflatable raft (unoccupied) floats down a river at an approximately constant speed of 5.6 m/s. a child on a bridge, 71 m above the river, sees the raft in the river below and attempts to drop a small stone onto the raft. the child releases the stone from rest. in order for the stone to hit the raft, what must be the horizontal distance between the raft and the bridge when the child releases the stone?

The equation that describes a transverse wave on a string is y = (0.0120 m)sin[(927 rad/s)t - (3.00 rad/m)x] where y is the displacement of a string particle and x is the position of the particle on the string. the wave is traveling in the +x direction. what is the speed v of the wave?

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.

An object moves from position +34m to the position -15m in 15 seconds. what is the total displacement? what is the total velocity?