2. Sally rolls a ball up to another person on a smooth ramp 19.6 m above her. The ball reaches the other person's hands when it is travelling 4.9 m/s uphill. If the ramp angle slows the ball
down by 3.7 m/s each second it travels up the ramp, find the initial velocity of the ball.

Take Sally's position to be the origin, and up-the-ramp to be the positive direction. The ball travels a distance x in time t of

x = u t + 1/2 (- 3.7 m/s²) t²

where u is the ball's initial velocity.

Its velocity v at time t is

v = u + (- 3.7 m/s²) t

Let T be the time it takes for the ball to reach the second person 19.6 m up the ramp. At this time, the ball attains a velocity of 4.9 m/s, so that

4.9 m/s = u + (- 3.7 m/s²) T

T = (u - 4.9 m/s) / (3.7 m/s²)

Substitute this into the distance equation, with x = 19.6 m, and solve for u :

19.6 m = u (u - 4.9 m/s) / (3.7 m/s²) + 1/2 (- 3.7 m/s²) ((u - 4.9 m/s) / (3.7 m/s²))²

u ≈ 13 m/s

the arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.

a longitudinal wave moves energy that is to the direction of the wave’s movement. - true