## Rate of Change Question1

In this page rate of change question1 we are going to see solution of some practice question of the worksheet.

Question 1:

A missile fired ground level rises x meters vertically upwards in t seconds and x = 100t- (25/2)t². Find

(i) the initial velocity of the missile,

(ii) the time when the height of the missile is a maximum

(iii) the maximum height reached and

(iv) the velocity with which the missile strikes the ground.

Solution:

x = 100t - (25/2)t²

(i) Since the missile starts initially the starting time must be zero

that is, t = 0

here distance is changing with respect to time,so we have to put the unit meter/seconds for the answer

dx/dt = 100 (1) - (25/2) (2t)

= 100 - 25 t

= 100 - 25 (0)

= 100 - 0

= 100 meter/seconds

(ii) the time when the height of the missile is a maximum

when a object reaches its maximum height the velocity will become zero.

dx/dt = 0

dx/dt = 100 - 25 t

100 - 25 t = 0

- 25 t = - 100

t = 100/25

t = 4 seconds

From this we can decide the object is taking 4 seconds to reach the maximum height.

(iii) the maximum height reached and

The missile is taking 4 seconds to reach its maximum height.

put t = 4

x = 100t - (25/2)t²

x = 100 (4) - (25/2) (4)²

= 400 - (25/2) (16)

= 400 - (25) (8)

= 400 - 200

= 200 meter

(iv) the velocity with which the missile strikes the ground

height of the missile = 0

x = 100t - (25/2)t²

100t - (25/2)t² = 0

- (25/2)t² = - 100 t

(25/2)t² = 100 t

t²/t = 100 (2/25)

t = 200/25

t = 8

to find the velocity of the missile we have to put 8 for t

dx/dt = 100 - 25 t

= 100 - 25 (8)

= 100 - 200

= -100 meter/seconds