Asoccer player with a mass of 60 kg is traveling at 8 m/s when he completes a corner kick on a 0.45 kg soccer ball. the soccer ball travels toward the goal at a speed of 35 m/s. in this elastic collision, what is the speed of the soccer player immediately after kicking the ball?
a) 5.4 m/s
b) 7 m/s
c) 7.7 m/s
d) 8 m/s

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

The horizontal blue line through the middle of the lens is called the optical axis. as the lamp is moved above or below the axis, keeping the horizontal distance to the center of the lens constant, how does the horizontal distance from the lens to the image change?

Madison lives near the ocean. she’s formed a hypothesis that increased concentrations of salt in the air speeds the corrosion of certain metals. if madison plans to test this hypothesis, she will have to deal with the following variables in her experiment: dependent variable: independent variable: one possible confounding variable: