Find the initial speed of the keys while they are thrown.
A student throws a set of keys vertically upward to her sorority sister in a window 4.0 m above. The keys are caught 1.50 s later by the sister's outstretched hand. With what initial speed were the keys thrown?
1. 10.0 m/s
2. 15.0 m/s
3. 13.7 m/s
4. 17.1 m/s
Determine time period of oscillation of a balloon.
a. A light balloon filled with helium of density 0.18 kg/m3 is tied to a light string of length L = 3m. The string is tied to the ground, forming an "inverted" simple pendulum. If the balloon is displaced somewhat from equilibrium, show that the motion is simple harmonic and decide the period of motion. Take the density of air to be 1.29 kg/m3.
b. Expectant parents are thrilled to hear their unborn baby's heart beat, revealed by an ultrasound motion detector. Assume the fetus's ventricular wall moves in simple harmonic motion with amplitude 1.80 mm and frequency 115 per minute. (i) Find out the maximum linear speed of the heart wall. Suppose the motion detector in contact with the mother's abdomen produces sound at precisely 2.00 MHz, which travels through the tissue at 1.50 km/s. (ii) Find out the maximum frequency at which the reflected sound is received by the motion detector. (By electronically listening for echoes, the detector can produce beeps of sound.)