To receive the most credit in each problem; show of all your work. You may find it helpful to use words to describe your logic. Clearly label which result is the answer to the question, ambiguities will result in loss of credit.
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1. There is a gap an uncompleted pedestrian bridge. A dare devil BMX cyclist wishes to put a ramp at one end of the gap to jump over the gap. They leave the ramp at 50 km/h and an angle of 40°. When they arrive on the other side the bridge is 50cm below the ramp height. What is the maximum distance the gap can be for a successful attempt?
2. A cyclist of 55kg (including the bicycle) approaches a stop sign and slows from 40 km/h to a stop over 50m. The pavement has an average coefficient of friction of 0.15. If the cyclist didn't use their brakes to slow down and simply expanded their surface area, what was the average drag force that slowed them down? A free body diagram and force table may help.
3. A boat in a current moves has initial r→i = (458i^ + 1000j^)m and v→i = (-5i^ + 6j^)m/s. If the boat accelerates for 10s with a→ = (18i^ - 50j^)m/s2, what is the boat's final r→f and v→f? After the acceleration the boat travels with constant velocity, if the water has a constant v→ = (-6i^ + 15j^)m/s, relative to Dock A. What is the boat's velocity relative to Dock A?
4. 2 Blocks of equal mass of 100kg are on a flat surface with a kinetic coefficient of friction of 0.27. They are connected by a massless magic string as shown below. What F→app is needed on Block A, such that a→ = -1.75m/s2? You must include a(the) Free Body Diagram(s) and Force Table(s) in your answer.
