Mechanics - PHYS 211 Homework 2 Problem 1: A rocket is launched straight up with constant acceleration. Four seconds after lifto (An = 4 s), a bolt falls off the side of the rocket The bolt hits the ground A12 : 6.0 s later. What was the rocket's acceleration. a? l; "'1 a) The motion of the bolt is shown in Fig. L The initial coordinate of the bolt, yo, is equal to the coordinate of the rocket at the moment when the bolt fell off, 3. and its initial velocity, 17.), is equal to the velocity of the rocket at that moment of time. First consider the motion of the rocket between the lioff and the moment when the bolt fell off. During that time, the rocket moves up with the constant accelera- tion a. Use the relevant equations from the constant-acceleration model to get the formulae for ya and no in terms of a and At]. .w -> O 3 FIG. 1: The scheme for Problem 1 b) After the bolt fell off, it moves with the free fall acceleration, Eff. Since the direction of the accel- eration (down) is opposite to the direction of the y-axis, the y-component of the acceleration is negative, affyy = 79.8 ms\". The second equation of the constant-acceleration model applied to the motion of the bolt becomes yf : yo+uuAtz + #1\Problem 3: A sprinter can accelerate with constant acceler- x x __ \">0 ation for 4.0 s before reaching top speed. He can run the 100 '4' *1 meter dash in 10.0 5. What is his speed, 0', as he crosses the 0 At? \"3 \"'51: 63 '0'\" nish line? FIG. 3: The scheme for Problem 3 a) As shown in the scheme, the motion of the sprinter consists of two parts. In part 1 (An = 4 5), he moves with a constant acceleration. In part 2 (At; = 6 5), he moves with a constant speed, and that is the speed with which he crosses the nish line. Suppose the acceleration of the sprinter in part 1 is a (we will not be concerned with its numerical value, but you can compute it later out of curiosity), What is the speed of the sprinter at the end of part 1. u', in terms of a and Atl (just write down the formula, without using numerical values)? b) Apply the second equation from the constant-acceleration model, Xf = x; + uiXAt + %a,(At)2, to both parts of the motion. 1 and 2. In the scheme, I used X], for the final coordinate of the sprinter in part 1, while xfz is the nal coordinate of the sprinter in part 2 (and for the entire run). Combining the two parts together and working with symbols only, show that the nal coordinate of the sprinter can he found from the formula )7; = U' (% + A12) c) Using the formula you found in part b), solve for 11' in terms ofoz, Atl and Atz, and nd its numerical value. (Answer: 12.5 m/s.)