A dump truck is being filled with sand. The sand falls straight downward from rest from a height of 2.00 m above the truck bed, and the mass of sand that hits the truck per second is 55.0 kg/s. The truck is parked on the platform of a weight scale. By how much does the scale reading exceed the weight of the truck and sand?

Water falls without splashing at a rate of $0.250L{s}^{-1}$ from a height of 2.60 m into a 0.750kg bucket on a scale. If the bucket is originally empty, what does the scale read 3s after water starts to accumulate in it?

The rear side of a truck is open. A box of $40kg$ mass is placed $5m$ away from the open end as shown in figure. The coefficient of friction between the box and the surface is $0.15$. On a straight road, the truck starts from rest and accel erating with $2m/s^2$. At what distance from the starting point does the box fall off the truck? Ignore the size of the box

A body of mass 2 kg falls 60 m from rest and is then brought to rest after penetrating $0.6$ m into some sand . Find the average thrust of the sand on it .

A $2-m$ wide truck is moving with a uniform speed $v_0=8m{s}^{-1}$ along a straight horizontal road. $A$ pedestrian starts to cross the road with a uniform speed $v$ when the truck is $4m$ away from him, The minimum value of $v$ so that he can cross the road safely is .

A box is put on a scale which is adjusted to read zero, when the box is empty. A stream of pebbles is then poured into the base from a height h above its bottom at a rate of n pebbles/s. Each pebble has a mass m. If the pebbles collide with the box such that they immediately come to rest after collision, then the scale reading at time t after the pebbles begin to fill the box is [ neglect piling up of pebbles]

A shot putter with a mass of $80kg$ pushes the iron ball of mass of $6kg$ from a standing position accelerating it uniformly form rest at an angle of ${45}^{\circ }$ with the horizontal during a time interval of 0.1 seconds. The ball leaves his hand when it $2m$ high above the level ground and hits the ground 2 seconds later $(g=10m/s^2)$.
The minimum value of the static coefficient of friction if the shot putter does not slip during the shot is closest to .

A block of mass 2.0 kg is pushed down an inclined plane of inclination ${37}^0$ with a force of 20N cting parallelto the incline. It is found tht the block moves on the incline with an acceleration of $10\frac{m}{s^2}$. If the blcok started from rest, find the work done a. by the applied force in the first second b. by the weight of the block in the first second and c. by the frictional force acting on the block in the first second. Take $g=10\frac{m}{s^2}$.

An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed $v_0$. In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g.
Just as the student starts his free fall, he presses the button of the stopwatch. When he reaches at the top of 100th floor, he has observed the reading of stopwatch as 00:00:06:00 (hh:mm:ss:100 th part of the second). Find the value of g. (correct upt ot two decimal places).

A 20kg box rests on the flat floor of a truck. The coefficients of friction between box and floor are ${\mu }_s$= 0.15 and ${\mu }_k$=0.10. The truck stops at a stop sign and then starts to move with an acceleration of $2\frac{m}{s^2}$. If the box is 2.2 m from the rear of the truck when the truck starts, how much time elapses before the box falls of fthe rear of the truck? How far does the truck travel in this time.

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of $2.2m/s^2$ and the automobile has an acceleration of $3.5m/s^2$. The automobile overtakes the truck when it (truck) has moved 60 m.
(a) How much time does it take the automobile to overtake the truck ?
(b) How far was the automobile behind the truck initially ?
(c) What is the speed of each during overtaking ?