A crate of weight $400 \mathrm{N}$ is lifted by a forklift truck. The truck lifts the crate from rest to a height of $2 \mathrm{m}$ in $5 \mathrm{s}.$ Assuming constant acceleration, find the normal contact force from the truck on the crate.

A force $F$ acts in a horizontal plane and has components $25 \mathrm{N}$ in the $x$ -direction and $-17 \mathrm{N}$ in the $y$ -direction relative to a set of axes. The force acts at an angle $\alpha$ below the $x$ -axis.

Find the sizes of $F$ and $\alpha .$

A force $F$ acts in a horizontal plane and has components $25 \mathrm{N}$ in the $x$ -direction and $-17 \mathrm{N}$ in the $y$ -direction relative to a set of axes. The force acts at an angle $\alpha$ below the $x$ -axis.

Another force has magnitude $29 \mathrm{N}$ and acts at an angle of $70°$ above the positive $x$ -axis. The resultant of these two forces has magnitude $R \mathrm{N}$ and makes an angle of $\theta$ with the positive $x$ -axis. Find the values of $R$ and $\theta .$

The graph shows the velocity of a parachutist as she falls from an aircraft until she hits the ground $50 \mathrm{s}$ later.

There are four stages to the motion: falling freely under gravity with the parachute closed; decelerating with the parachute open; falling at constant speed with the parachute open; and coming to rest instantaneously on hitting the ground.

Find the total distance fallen.

The graph shows the velocity of a parachutist as she falls from an aircraft until she hits the ground $50 \mathrm{s}$ later.

There are four stages to the motion: falling freely under gravity with the parachute closed; decelerating with the parachute open; falling at constant speed with the parachute open; and coming to rest instantaneously on hitting the ground.

The parachutist has mass $70 \mathrm{kg}.$ Show that the upward force on the parachutist due to the parachute during the second stage is $1148 \mathrm{N}.$

A particle of mass $6.3 \mathrm{kg}$ is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point $X.$ It is held in equilibrium by a horizontal force $F$ when the string is at an angle $\alpha$ to the vertical, where $\tan \alpha =\frac{20}{21}.$ Find the tension in the string and the size of $F.$

A particle $P$ is in equilibrium on a smooth horizontal table under the action of four horizontal forces of magnitudes $6 \mathrm{N}, 5 \mathrm{N}, F \mathrm{N}$ and $F \mathrm{N}$ acting in the directions shown. Find the values of $\alpha$ and $F.$