1989 Nov. G.C.E Homework
When a stone is thrown vertically upwards, it’s distance (d metres) after t seconds is given by the formula d=60t-10t². For values of t from 1 to 5 seconds using 2cm to 1unit on the t axis and 2cm to 20units on the d-axis. Calculate your graph
(I) how long does it take to reach a height of 70 metres? (II) determine the height of the stone after 5 seconds (III) after how many seconds does it reach to it maximum height (IV) determine the slope of the graph when t = 5 seconds
Solution
Solution
First we’ve to find distance d(meters)
Formula d = 60t-10t²,
For values of t from 1 to 5 seconds
When t = 1
distance d (meters) = 60t-10t²
60(1)-10(1)² = 60-10
50( distance is 50 when time is 1 second)
When t = 2
distance d (meters) = 60t-10t²
60(2)-10(2)² = 120-10(4)
120-10×4 = 120-40
80( distance is 80 when time is 2 second)
When t = 3
distance d (meters) = 60t-10t²
60(3)-10(3)² = 180-10×9
180-90 = 90 ( distance is 90 when time is 3 second)
When t = 4
distance d (meters) = 60t-10t²
60(4)-10(4)² = 240-10×16
240-160 = 80( distance is 80 when time is 4 second)
When t=5
distance d (meters) = 60t-10t²
60(5)-10(5)² = 300-10×25
300-250 = 50 ( distance is 50 when time is 5 second)
Plot a graph of distance against time ( where distance(d metres) will be y axis and time ( t seconds) will represent x axis
Let y represent 20cm at 2units
And let X represent 1cm at 2units
How to plot graph of d(metres) against t (secs)
Watch this video
(I) how long does it take to reach a height of 70 metres?
It takes 1.5secs to reach 70 metres
(II) determine the height of the stone after 5 seconds
The height of the stone after 5 seconds is 50 metres
(III) after how many seconds does it reach to it maximum height
After 3 seconds
(IV) determine the slope of the graph when t = 5 seconds
y2-y1/x2-x1 = 50-30/5-3
10m/s
