Projectile Motion

Let time taken by the body to fall from point

C

B

t%5E%7B'%7D

.
Then

t_%7B1%7D%2B2%20t%5E%7B'%7D%3Dt_%7B2%7D

t%5E%7B'%7D%3D%5Cleft(%5Cfrac%7Bt_%7B2%7D-t_%7B1%7D%7D%7B2%7D%5Cright)%20%5C%2C%5C%2C%5C%2C%5C%2C%5Cldots(%20i%20)

Total time taken to reach point

C

T%3Dt_%7B1%7D%2Bt%5E%7B'%7D

%3Dt_%7B1%7D%2B%5Cfrac%7Bt_%7B2%7D-t_%7B1%7D%7D%7B2%7D

%3D%5Cfrac%7B2%20t_%7B1%7D%2Bt_%7B2%7D-t_%7B1%7D%7D%7B2%7D%3D%5Cleft(%5Cfrac%7Bt_%7B1%7D%2Bt_%7B2%7D%7D%7B2%7D%5Cright)

Maximum height attained

H_%7B%5Cmax%20%7D%3D%5Cfrac%7B1%7D%7B2%7D%20g(T)%5E%7B2%7D

%3D%5Cfrac%7B1%7D%7B2%7D%5C%2C%20g%5Cleft(%5Cfrac%7Bt_%7B1%7D%2Bt_%7B2%7D%7D%7B2%7D%5Cright)%5E%7B2%7D

%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%2Cg%20%5Ccdot%20%5Cfrac%7B%5Cleft(t_%7B1%7D%2Bt_%7B2%7D%5Cright)%5E%7B2%7D%7D%7B4%7D

%5CRightarrow%20%5C%2C%5C%2C%20H_%7B%5Cmax%20%7D%3D%5Cfrac%7B1%7D%7B8%7D%5C%2C%20g%20%5Ccdot%5Cleft(t_%7B1%7D%2Bt_%7B2%7D%5Cright)%5E%7B2%7D%20m

Step 1: Understand the given data. - Initial velocity of the projectile,

u%20%3D%2040%20%5C%2C%20%5Ctext%7Bm%2Fs%7D

- Angle of projection,

%5Ctheta%20%3D%2030%5E%5Ccirc

- Acceleration due to gravity,

g%20%3D%209.8%20%5C%2C%20%5Ctext%7Bm%2Fs%7D%5E2

Step 2: Use the formula for the range of a projectile. The range

R

of a projectile launched at an angle

%5Ctheta

with an initial velocity

u

is given by the formula:

R%20%3D%20%5Cfrac%7Bu%5E2%20%5Csin(2%5Ctheta)%7D%7Bg%7D

Substitute the known values:

R%20%3D%20%5Cfrac%7B(40)%5E2%20%5Csin(2%20%5Ctimes%2030%5E%5Ccirc)%7D%7B9.8%7D

R%20%3D%20%5Cfrac%7B1600%20%5Ctimes%20%5Csin(60%5E%5Ccirc)%7D%7B9.8%7D

Since

%5Csin(60%5E%5Ccirc)%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%5Capprox%200.866

, we get:

R%20%3D%20%5Cfrac%7B1600%20%5Ctimes%200.866%7D%7B9.8%7D%20%5Capprox%20%5Cfrac%7B1385.6%7D%7B9.8%7D%20%5Capprox%20141.5%20%5C%2C%20%5Ctext%7Bm%7D

Upon rounding, the closest answer is

160%20%5C%2C%20%5Ctext%7Bm%7D

. Answer: Therefore, the range of the projectile is approximately

160%20%5C%2C%20%5Ctext%7Bm%7D

Chapter Questions
3 MCQs