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A child of mass 30 kg slides from rest down a wooden pole by a distance of 3.0 m. Calculate the average force of friction acting on the child if her speed is 1 2.0 ms when she hits the ground. Take 2 g 10 ms .
Two cars are driving toward each other on a straight and level road. One car is traveling at 100 km/h north and the other car is traveling at 42.0 km/h south, both velocities measured relative to the road. At a certain instant, the distance between the cars is 10.0 km. How long will take for the two cars to meet?
A horizontal frictionless table has a small hole in its center. Block A on the table is connected to block B hanging beneath by a string of negligible mass which passes through the hole. Initially, B is held stationary and A rotates at constant radius 𝑟𝑟0 with steady angular velocity 𝜔𝜔0. (a) (2 marks) Draw a free body diagram of all the mobile bodies.
(b) (3 marks) Find the radial and tangential component of the acceleration of block A.
(c) (5 marks) Find the acceleration of block B immediately after the release. Also find the tension in the string.
An object moves along the x axis according to the equation x(t)= (3.00t 2 - 2.00t + 3.00) m, where t is in seconds. Determine
(a) the instantaneous velocity at t = 2.00 s and t = 3.00 s,
(b) the average acceleration between t = 2.00 s and t = 3.00 s,
(c) the instantaneous acceleration at t = 3.00 s
Find the beat frequency when a 386 Hz and a 389 Hz tuning fork are struck at the same time.
Calculate,(1).The maximum speed of the pendulum.(2). The maximum acceleration of the Bob
An object (m=0.5kg) is moving along x-axis with v0 = 1.6m/s. At t =0s, at which object is at thr origin, a force directed along the negative x-axis F = -kt^3 starts to apply to it. At t=2s, the object passes the origin again. Find k ( a constant).
Q6. Find the gradient of the following functions
f(x, y, z) = x2y3z4.
f(x, y, z) = exsin(y) ln(z).
Q7. The height of certain hill (in feet) is given by h(x,y)=10(2xy−3x2 −4y2 −18x+28y+12)
Where y is the distance in north, x is the distance in east.
a. Where is the top of the hill located?
b. How high is the hill?
c. How steep is the slope (in feet per mile) at a point 1-mile north and 1- mile east, in what
direction is the slope steepest?
Q8. Calculate the divergence and Curl, of the following functions
a. V= x2 i+3xy^2 j -2xyz k
b. V=xyi+2yz j+3zx k
c. V= y2i +(2xy+z2)j+ 2yz k , where i , j , k are unit vectors along x, y and z axis
