The acceleration of gravity can be measured by projecting a body upward and measuring the time that it takes to pass two given points in both directions. Show that if the time the body takes to pass a horizontal line A in both directions is TA, and the time to go by a second line B in both directions is TB, then assuming that the acceleration is constant, its magnitude is g = 8h / ((TA)2 - (TB)2) where h is the height of line B above line A.
The acceleration of gravity can be measured by projecting a body upward and measuring the time...
Note: Show this using kinematic equations,
please.
The acceleration due to gravity g near the surface of the Earth can be measured by projecting an object vertically upward and measuring the time that it takes to pass two given points in both directions. See the diagram below. Notice that the horizontal axis is time not position the path of the object is purely along a straight, vertical line. Show that if the time the body takes to pass a horizontal...
3. The acceleration due to gravity by dropping a baseball and measuring the time T it takes for the 2D Suppose that both D and T are measured ball to travel a measured vertical distance D is G = 432 ft, V(D) = 0.02 ft2, E(T) = 5.2 sec and V(T) independently with errors so that E(D) 0.003 sec2 Compute approximate values for E(G) and V(G) by propagation of error. a. b. What percent of the variance V(G) is due...
2. An aspiring juggler realizes that the acceleration due to gravity can be measured simply by comparing the time interval an object spends above a certain height when tossed vertically upwards to the total time it is in the air. Suppose she tosses a small ball vertically upwards and catches it a moment later (after a time ∆T elapses) at the same height it was released. In flight, the ball spends a time interval ∆t above a certain height H...
2: For this problem the heights are low enough that the acceleration due to gravity can be approximated as -g. (Note: even at low Earth orbit, such as the location of the International Space Station, the acceleration due to gravity is not much smaller then g. The apparent weightlessness is due to the space station and its occupants being in free-fall.) A rocket is launched vertically from a launchpad on the surface of the Earth. The net acceleration (provided by...
A rocket, initially at rest on the ground, accelerates straight upward with constant net acceleration, from time t=0 until, at which time the fuel is exhausted. Neglect air resistance and assume that the rocket stays close enough to the ground that the acceleration due to gravity (after the rocket engine stops) is given by g. a) Find the maximum height, h, that the rocket reaches above the ground. b) Find the total time of flight, that the rocket is in...
A 50kg skydiver jumps out of an airplane. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude cv^2 where c=.1275 kg/m and is the velocity of the skydiver at time t (and upward is positive velocity). The gravitational constant is 9.8 m/s^2 . a) Find a differential equation for the velocity. b) Determine the terminal velocity in...
An object moving in the *x direction experience an acceleration of *2.0 m/s^2- This mean the object is increasing its velocity by 2.0 m/s every second. travels 2.0 m In every second. is traveling at 2.0 m/s. is decreasing its velocity by 2.0 m/s every second. Suppose that an object is moving with a constant velocity. Which statement concerning Its acceleration must be correct? The acceleration is constantly increasing. The acceleration is a constant non-zero value. The acceleration is constantly...
A 7500-kg rocket blasts off verti- cally from the launch pad with a constant upward acceleration of 2.25 m>s 2 and feels no appreciable air resistance. When it has reached a height of 525 m, its engines suddenly fail; the only force acting on it is now gravity. (a) What is the maximum height this rocket will reach above the launch pad? (b) How much time will elapse after engine failure before the rocket comes crashing down to the launch...
A. Alhouse is thrown straight upward off a high building. The building is located somewhere on the surface of Earth. 4 seconds later, the mouse hits the ground. ASSUME: • The building is an unknown height. • The mouse takes 4 seconds to reach the ground. • The mouse's initial speed is 5 m/s DETERMINE: • The height of the building. 6 pts) B. Near the surface of Earth, a helicopter travels upward at a constant velocity. At some moment,...
A particular cat flea (Ctenocephalides felis) has a mass of 5.0 x 10kg. Like most fleas, this one can jump many times higher than its own height. When jumping, it accelerates from rest through a distance of 0.40 mm, which allows it to reach a launch speed of 1.2 m/s, directed straight up. Use g = 9.8 m/s. [2 points] (a) Assuming constant acceleration, calculate the magnitude of the flea's acceleration while it is accelerating upward. [2 points] (b) For...