A pumpkin of mass 5 kg shot out of a student-made cannon under air pressure at an elevation angle of 45° fell at a distance of 142 m from the cannon. The students used light beams and photocells to measure the initial velocity of 54 m/s. If the air resistive force was F = -kmv, what was the value of k?

The "classical" radius of a neutron is about 0.81 fm (1 femtometer = 10-15 m). The mass of a neutron is 1.675×10-27 kg.  a) Assuming the neutron is spherical, calculate its density in kilograms per cubic meter.   b) What would be the magnitude of the acceleration due to gravity, in meters per second squared, at the surface of a sphere of radius R = 1.2 m with this same density? Recall that the gravitational constant is G = 6.67 × 10-11 m3/kg/s2.

In a later chapter, you will find that the weight of a particle varies with altitude such that w=mgr02r2where r0is the radius of Earth and ris the distance from Earth’s center. If the particle is fired vertically with velocity v0from Earth’s surface, determine its velocity as a function of position r. (Hint: use adr=vdv, the rearrangement mentioned in the text.)

Check Your Understanding Consider the density required to make Earth a black hole compared to that required for the Sun. What conclusion can you draw from this comparison abut what would be required to create a black hole? Would you expect the Universe to have many black holes with small mass?

What is the theoretical value for how long it would take a metal ball to fall 1.5 meters in the Free Fall ApparatusExperiment?

Assuming we take several trials where the total mass ?1+?2 is constant, but we redistribute themasses between ?1 and ?2.  The equation you derived as your answer to the Problem (2) would apply. (a) Assume that we took these trials and plottedthe difference in the weights,??−??, on the ?-axis and the accelerationon the ?-axis. What would be the theoretical value–that is, in terms of other known quantities –of the slope?(Once again, you can think of this in terms of your equation answer to the previous problem. (b) For the same plot, what would be the theoretical value of the intercept? (c)Now consider if there were another constant force in the equation, such as friction. What would the theoretical value of the interceptbe in this case? (justify)

Problem 6: During service, a tennis ball is struck at height h = 1.8 m above a tennis court and moves with velocity vo = vo,i. Assume the ball encounters no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position. Randomized Variables h = 1.8 m Vox = 20.5 m/s Part (a) Calculate the tennis ball's horizontal velocity, v in m/s, when it strikes the court. Numeric : A numeric value is expected and not an expression. Vfx = Part (b) How long, tç in seconds, does the tennis ball move before striking the court? Numeric : A numeric value is expected and not an expression. ケ= Part (c) How far horizontally from the service position, x,in meters, does the tennis ball move before striking the court? Numeric : A numeric value is expected and not an expression. * =

Using alternate form of the Torricelli law. What isthe theoritical time to empty a hemispherical tank (flat side at the bottom) is full of H2O of radius 1 m. It has a bottom hole of radius 1 cm. If this bottom hole is opened at 1 PM. Proved the answer 02:00:14 PM.

b): The patcutal 0.21 partile a abag the X-aris is Ulx)=822x" is Where Joules meters.2Iher is Dill be and the at Xelom, in in That acelention,

Why was m converted to cm?