Asphere 5 cm in diameter has a small scratch on its surface. when the scratch is viewed through the glass from a position directly opposite, where does the scratch appear and what is its magnification? assume n = 1.5 for the glass.

Matt is driving down 7th street. he drives 150 meters in 18 sec. assuming he doesn’t slow down or speed up, what is his speed?

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 record distance in the sport of throwing cowpats is 81.1 m. this record toss was set by steve urner of the united states in 1981. assuming the initial launch angle was 45° and neglecting air resistance, answer the following. (a) determine the initial speed of the projectile. m/s