Motion in Two Dimensions

Velocity is a vector quantity because it has both magnitude and direction.

Displacement is the change in the position of an object from its initial position to its final position.

Acceleration is the rate of change of velocity of an object.

The equation of motion in two dimensions is $s = ut + 1/2 at^2$.

The maximum height reached by the projectile is given by the equation $h = (u^2 sin^2 \theta)/(2g)$. Substituting the values, we get $h = (10^2 sin^2 30)/(2 * 9.8) = 10 m$.

The time taken by the ball to reach its maximum height is given by the equation $t = u/g$. Substituting the values, we get $t = 10/9.8 = 2 s$.

The velocity of the ball just before it hits the ground is given by the equation $v = sqrt(2gh)$. Substituting the values, we get $v = sqrt(2 * 9.8 * 100) = 40 m/s$.

The distance travelled by the car in 1 hour is given by the equation $s = vt$. Substituting the values, we get $s = 60 * 1 = 60 km$.

The time taken by the train to travel a distance of 180 km is given by the equation $t = s/v$. Substituting the values, we get $t = 180/90 = 2 hours$.

The distance travelled by the boat in 5 minutes is given by the equation $s = vt$. Substituting the values, we get $s = 10 * 5 * 60 = 300 m$.

The time taken by the cyclist to travel a distance of 10 km is given by the equation $t = s/v$. Substituting the values, we get $t = 10/15 = 40/60 = 40 minutes$.

The distance travelled by the car in 1 hour is given by the equation $s = vt$. Substituting the values, we get $s = 60 * 1 = 60 km$.

The time taken by the train to travel a distance of 180 km is given by the equation $t = s/v$. Substituting the values, we get $t = 180/90 = 2 hours$.

The distance travelled by the boat in 5 minutes is given by the equation $s = vt$. Substituting the values, we get $s = 10 * 5 * 60 = 300 m$.

The time taken by the cyclist to travel a distance of 10 km is given by the equation $t = s/v$. Substituting the values, we get $t = 10/15 = 40/60 = 40 minutes$.