Gravity Motion Problem: Analyzing Velocity and Distance

A body is thrown up with a velocity 100 ms^-1. It travels 5 m in the last second of its journey.If the same body is thrown up with a velocity 200 ms^-1, how much distance (in metre) will it travel in the last second? (take g=10 ms^-2)

Question:

Solution: Distance travelled in the last second when thrown with a velocity 200 ms^-1

Initial velocity u=200 ms^-1

Distance travelled during the 20^th second:

$${h=ut-\frac{1}{2}gt^2}$$

$${h(20 \ sec)=200(20)-\frac{1}{2}(10)20^2}$$

$${h(20 \ sec) =4000-(5)(400)}$$

$${h(20 \ sec)=2000 \ m}$$

Distance travelled during the 19^th second:

$${h(19 \ sec)= 200(19)-5(361)}$$

$${h(19 \ sec) =3800 -1805}$$

$${h(19 \ sec)=1995}$$

Distance travelled during the last second

$${h(20 \ sec) -h(19 \sec)=2000-1995}$$

$${=5 \ m}$$

The distance travelled in the last second of its journey when thrown with initial velocity of 200 ms^-1 is 5 m