Question

1. Constant Acceleration -1g Spaceship. Imagine that a spaceship can accelerate (starting from rest) at a sustained 1 g (9.8 m/sec') for any desired length of time. Make a table as follows Elapsed time 1 minute 1 hour dadayS 1 week (7 days) 1 month (30 days) m/sec km/sec km/sec km/sec km/sec Distance Travel meters kilometers millions of kilometers billions of kilometers billions of kilometers For each listed time, calculate both the attained velocity and the distance traveled. (The numbers will become very big very quickly. Convert into the appropriate units given.) 2. Skyscraper. An object is dropped from a skyscraper 250 meters high. Disregarding air resistance calculate a) the time to fall to the ground, and b) the impact velocity 3. Rocket Sled. A rocket sled accelerates at 2.8 g through 32 meters. a) What is the final velocity of the sled? b) How long does the ride last? (In the earliest days of the Space Race, people rode these things. You can find the videos on YouTube.) In this problem, use g = 10.0 m/sec' 4. Tossed Ball. A ball is tossed upward with an initial velocity of 9.8 m/sec. How high does the ball reach (above the launch height)? 5. Time of Flight. The same ball is tossed upward again with v, 9.8 m/sec, but from an initial height of 2.0 meters. The ball impacts the ground. How long does this take? 6. Mathematical Model of a Track Runner. The velocity of track runners can be well-modeled by the function where Vam is the upper lit of the runner's speed, and k is a model parameter (also a constant). a) Graph the general appearance of this function. b) Integrate this function w/r/t time from t-0 to t t to yield the distance traveled as a function of time. c) A race runs 100 meters. Given k- 0.852 sec 11.2 m/sec, find the value of t, that gives the result closest to 100 meters

Answer 1

2,

(a)

From kinematic equation,

h = ut - (1/2)gt^2

Since, object is dropped, u = 0

250 = 0 - (1/2)*9.8*t^2

t = 7.14 s

(b)

Impact velocity of the object,

v = u + gt

v = 0 + 9.8*7.14

v = 70 m/s