He hobbits are building a watchtower so they can prepare to battle in case trolls decide to attack them. one hobbit will always be on the lookout and the hobbits will prepare for battle as soon as the trolls are visible. the time, ttt, in minutes, that the hobbits have to prepare for the attack of trolls kkk meters away is given by the function t(k)=\dfrac{k}{80}t(k)= 80 k t, left parenthesis, k, right parenthesis, equals, start fraction, k, divided by, 80, end fraction. the visibility, vvv, in meters, that the hobbits have from an mmm meter watch tower is given by the function v(m)=50mv(m)=50mv, left parenthesis, m, right parenthesis, equals, 50, m. find an explicit expression that models the amount of time the hobbits have to prepare for a troll attack given that the watchtower is mmm meters tall.

Avery hard rubber ball (m = 0.5 kg) is falling vertically at 4 m/s just before it bounces on the floor. the ball rebounds back at essentially the same speed. if the collision with the floor lasts 0.05 s, what is the average force exerted by the floor on the ball?

The x-coordinate of a particle in curvilinear motion is given by x = 3.1t3 - 4.9t where x is in feet and t is in seconds. the y-component of acceleration in feet per second squared is given by ay = 2.3t. if the particle has y-components y = 0 and vy = 5.0 ft/sec when t = 0, find the magnitudes of the velocity v and acceleration a when t = 1.8 sec. sketch the path for the first 1.8 seconds of motion, and show the velocity and acceleration vectors for t = 1.8 sec. answers: v = ft/sec a = ft/sec2

Askydiver weighing 140 lb (including equipment) falls vertically downward from an altitude of 19,000 ft and opens the parachute after 18 s of free fall. assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.55|v| when the parachute is closed and is of magnitude 14|v| when the parachute is open, where the velocity v is measured in ft/s. assume that acceleration due to gravity has magnitude 32 ft/s/s; remember that weight is the product of mass and gravitational acceleration. (a) find the speed of the skydiver when the parachute opens. (b) find the distance fallen before the parachute opens. (c) what is the limiting velocity vl after the parachute opens? (d) determine how long the sky diver is in the air after the parachute opens. (e) plot the graph of velocity versus time from the beginning of the fall until the skydiver reaches the ground.