Here are the calculations: Given: Initial velocity, $u = 30 \, \text{m/s}$ Acceleration due to gravity, $g = 10 \, \text{m/s}^2$ (acting downwards) At the highest point, the final velocity, $v = 0 \, \text{m/s}$. a) The time taken to reach its highest point: Step 1: Use the kinematic equation relating initial velocity, final velocity, acceleration, and time. Since the ball is moving upwards against gravity, the acceleration is $-g$. $$v = u - gt$$ Step 2: Substitute the known values into the equation. $$0 = 30 \, \text{m/s} - (10 \, \text{m/s}^2)t$$ Step 3: Solve for $t$. $$10t = 30$$ $$t = \frac{30}{10}$$ $$t = 3 \, \text{s}$$ The time taken to reach the highest point is $\boxed{\text{3 s}}$. b) The distance travelled: Step 1: Use the kinematic equation relating initial velocity, final velocity, acceleration, and displacement. $$v^2 = u^2 - 2gs$$ Step 2: Substitute the known values into the equation. $$0^2 = (30 \, \text{m/s})^2 - 2(10 \, \text{m/s}^2)s$$ $$0 = 900 \, \text{m}^2/\text{s}^2 - 20s \, \text{m/s}^2$$ Step 3: Solve for $s$. $$20s = 900$$ $$s = \frac{900}{20}$$ $$s = 45 \, \text{m}$$ The distance travelled to the highest point is $\boxed{\text{45 m}}$.