1 On a very muddy football field a 110kg linebacker tackles

1) On a very muddy football field, a 110-kg linebacker tackles an 85-kg halfback. Immediately before the collision, the linebacker is slipping with a velocity of 8.5 m/s north and the halfback is sliding with a velocity of 7.2 m/s east. What is the velocity (magnitude) at which the two players move together immediately after the collision? What is the direction of this velocity? 2) A spring of negligible mass has a force of k= 1600 N/m a.) How far must the spring be compressed for 3.20 J of potential energy to be stored in it? b.) you place the spring vertically with on end on the floor. you then drop a 1.20 kg book onto it from a height of 0.880 m above the top of the spring. c.) Find the maximum distance the spring will be compressed. 3) Use the work-energy theorem to solve each of these problems. You can use Newton\'s laws to check your answers, A skier moving at 5.00 m/s encounters a long, rough horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis. A) How far does she travel on this patch before stopping? B) Suppose the rough patch in part was only 2.90 m long. How fast would the skier be moving when she reached the end of the patch? C) At the base of a frictionless icy hill that rises at 25.0 degree above the horizontal, a toboggan has a speed of 12.0 m/s toward the hill. How high vertically above the base will it go before stopping?

Solution

p₁ = m₁ v₁ = 110 * 8.5 = 935

p₂ = m₂ v₂ = 85 * 7.2 = 612

P = sqrt (935² + 612²) = 1117.48 kg.m/s

M = M₁ + M₂ = 195 kg

velocity of the combination V = 1117.48 / 195 = 5.73 m/s

Let the direction of P make an angle theta with the N direction

tan theta = 612 / 935 = 0.655

theta = 33.22 deg