Problem 1)
I don't understand how they got the answers for A) and B) :
Ima Rushin can travel from Milwaukee Avenue to the school entrance gate at a constant speed of 22.5 m/s when the lights are green and there is no traffic. On Wednesday, Ima is stopped by a red light at Landwehr Road. She decelerates at -3.95 m/s/s, waits for 45.0 seconds before the light turns green and accelerates back up to speed at 4.91 m/s/s.
a. Determine the total time required to decelerate, stop and accelerate back up to speed.
b. Determine the amount of time the red light costs the driver (compared to if the car had not been stopped by the red light).
Answers:
a. 55.3 sec
b. 50.1 sec
Problem 2) A tortoise and a hare are having a 1000-meter race. The tortoise runs the race at a constant speed of 2.30 cm/s. The hare moves at an average speed of 1.50 m/s for 10.0 minutes and then decides to take a nap. After waking up from the nap, the hare recognizes that the tortoise is about to cross the finish line and immediately accelerates from rest with a constant acceleration of 0.500 m/s/s for the remaining distance of the race. If the tortoise wins by a hair (no pun intended), then what is the time in hours that the hare napped?
Answer:11.9 hr (How?)
Problem 3)Hayden and Matthew are riding around the neighborhood on their scooters. Hayden is at rest when Matthew passes him moving at a constant speed of 0.37 m/s. After 1.8 seconds, Hayden decides to chase after Matthew, accelerating at 0.91 m/s/s. How much time must Hayden accelerate before he is side-by-side with Matthew?
(How to even begin the problem) but here is the Answer: 1.7 s (rounded from 1.68 s)
2 answers
T1 = -Vo/a = -22.5/-3.95=5.70 s To stop.
V = Vo + a*T2 = 22.5.
T2 = (22.5-Vo)/a = (22.5-0)/4.91=4.58 s.
To accelerate back up to speed.
T1+45+T2 = 5.70 + 45 + 4.58 = 55.3 s.
2. Hare:
r*t = 1000.
1.5t = 1000.
t = 666.67 s., Non-stop.
Tortoise:
r*t = 1000.
0.023t = 1000.
t = 43,478.3 s.
Hare: 43,478.3 - 666.66 = 42,811.6s = 11.9 h. Sleeping.
3. Matthew: d = r*t = 0.37m/s * 1.8s = 0.666 m. Head-start.
0.5*0.91*t^2 = 0.37t + 0.666.
0.455T^2 - 0.37t - 0.666 = 0.
Use Quadratic Formula.
t = 1.683 s.
3 answers