Questions asked by Ridinion K.
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The displacement s, measured in meters for a body moving from a fixed point,
P, at a time of t seconds is given by #s(t) = 105te^(t/10)#. Determine the expression for the velocity v(t)?

Using logarithmic differentiation or otherwise, differentiate x^(x^2)?

Show #y=cos2xe^x# is a solution to the differential # (d^2y)/(dx^2) + 2dy/dx+5y = 0 #?

A volume of a cone is given by #V=(pir^2h)/3#. A particular cone has a height equal to five times the radius of its base: #h=5r#....? (continued below)

How do you find #x# for #1lnx#?

A firework rocket takes off vertically with an acceleration of #20ms^2# and
maintains that acceleration for 5 seconds after which the rocket stops burning. Find (a), (b) and (c), below?

On an alien planet, a ball is thrown vertically upwards from the ground, rises
to a height of 100 m, and then falls back to the ground. The total time is taken
from when the ball was thrown upwards to when it reached the ground again,
is 10 seconds.....?

The bulk modulus of lead is #4.6# GPa. By what fraction will the density of a
piece of lead increase if it is lowered to the bottom of the Pacific Ocean where
the pressure is #40# MPa?

A ball has a kinetic energy of 100 J. What would be the kinetic energy of a ball with twice the mass and half the momentum?

A cubical box consists of 4 square sides and a square base but has no top.
The sides and the base are all made of thin sheet metal of uniform thickness.
If the edges of the box are all 200 mm in length, how far above the base is the
box’s centre of mass?

How much kinetic energy is lost in the collision? (See full question below)

A shell fired from a gun has a horizontal range of 1200 m and a flight time of 10 s. What is the magnitude and direction of the velocity of projection?

Two forces, A and B, have a resultant C. (In other words A + B = C, as vectors). If A = 5 N, B = 7 N and C = 8 N, what is the angle between A and C?

What is the final velocity of the lighter object? (See below)

The Moon has a radius of #1737 km# and the gravitational acceleration at its
surface is #1.62ms^2#. Assuming that the Moon is a sphere of uniform
density, what is its density?

A rocket with a total mass of #20 kg# will take off with an acceleration
of #12 ms^2# if it is launched so that its trajectory is vertically upward. a) Calculate the force produced by the rocket engine? (please check below for part b)

Three forces P, Q and R act at the same point and are in equilibrium. The
forces P and Q have magnitudes 30 N and 20 N respectively, and there is an
angle of 20° between their directions. Calculate the magnitude of the force R?

An object has a kinetic energy of 500 J due to its linear motion. What would be the kinetic energy of an object with half the mass and twice the momentum?

An electron with a velocity of #1×10^7 ms^1# enters a magnetic field of strength #10 T# aligned perpendicular to the direction of motion of the electron. Calculate the radius of the orbital path that the electron now follows?

A block of mass 5 kg is at rest on a ramp which is at 25◦. The coefficient of static friction between the block and the slope is 0.4. What is the minimum magnitude of the horizontal force, F, that is required to make the block move? Assume #g=10ms^2#

A car accelerates uniformly from rest along a straight road until it reaches #50ms^1#. Once this speed is reached it immediately starts to decelerate uniformly until stationary again. If the total distance travelled is 600m, how long does journey take?

What is the coil current 2ms after being connected to the supply if a coil of inductance 0.5H and resistance 500#Omega# is connected across a 250V DC supply? (The time constant T of the circuit is 1ms).

A 5m length of conducting wire has overall resistance 2#Omega# with current flowing through it. It dissipates 8W of power along its length. Wire contains #8*10^22# free electrons. Calculate the average drift velocity of the electrons?

PARTIAL DERIVATIVE: Compute #(del^2g)/(delxdely)# and #(del^2g)/(delydelx)# for the function #g(x,y)=(1+y^2)e^(x^2y)# and show that they are both equal?

What are the equations of the tangent and the normal to the curve #y=cos(2x)e^x# at the point where #x=0#?

A coil possessing both inductance L and resistance R is connected to a 24V
dc supply having negligible internal resistance. The dc current in this circuit is found to be 3A. When the coil is connected to a 24V, 50Hz ac supply with negligible internal....?