Cars A and B are racing each other along the same straight road in the following
ID: 1689629 • Letter: C
Question
Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance D_A beyond the starting line at t = 0. The starting line is at x=0. Car A travels at a constant speed v_A. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed v_B, which is greater than v_A.1)How long after Car B started the race will Car B catch up with Car A?
2)How far from Car B's starting line will the cars be when Car B passes Car A?
B)In this problem, you will apply kinematic equations to a jumping flea. Take the magnitude of free-fall acceleration to be 9.80 m/s^2. Ignore air resistance.
1)A flea jumps straight up to a maximum height of 0.450 m. What is its initial velocity v_0 as it leaves the ground?
2)How long is the flea in the air from the time it jumps to the time it hits the ground?
Explanation / Answer
Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance D_A beyond the starting line at t = 0. The starting line is at x=0. Car A travels at a constant speed v_A. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed v_B, which is greater than v_A. 1)How long after Car B started the race will Car B catch up with Car A? find time t A's displacement dA = vA*t B's displacement dB = vB*t we have dB = dA + D_A vB*t = vA*t + D_A so t = D_A/(vB - vA) 2)How far from Car B's starting line will the cars be when Car B passes Car A? dB = vB*t = vB*D_A/(vB - vA) B) 1) h = 0.450 m. find initial velocity v_0. final velocity = 0 0^2 - v_0^2 = 2(-g)h so v_0 = sqrt(2gh) = 2.97 m/s 2) during time t, displacement = 0 = v*t - gt^2/2 t = 2v/g = 0.606 s