A projectile is fired at an angle of 60degree with the horizontal and with the initial velocity 80m/s calculate (a) the time of flight(b)time to reach maximum height(c)it range(d)the velocity of projection 2seconds after been fired
a)T=2u sin60/g=13.85s
b)t=T/2=6.92s
c)R=554.25m
A projectile is fired from ground level with an initial velocity of 50m/s and an initial angle of 30degree. Assuming g= 9.8 m/s*2, find:
(a) The projectile total time of flight.
(b) The maximum height attained
(c) The total horizontal traveled
(d) The final horizontal and vertical velocities just before it hits the ground
To solve this problem, we can use the equations of motion for projectile motion. Let's break down each part of the question:
(a) The time of flight:
The time of flight refers to the total time it takes for the projectile to reach the ground. We can calculate this using the following formula:
Time of flight = (2 * initial velocity * sin(angle)) / g
Substituting the given values:
Initial velocity = 80 m/s
Angle = 60 degrees
g = acceleration due to gravity = 9.8 m/s^2
Time of flight = (2 * 80 * sin(60)) / 9.8
Calculate the value using a calculator to get the answer.
(b) Time to reach maximum height:
To find the time taken to reach the maximum height, we need to use the formula for vertical motion:
Time to reach maximum height = initial velocity * sin(angle) / g
Substituting the given values:
Time to reach maximum height = 80 * sin(60) / 9.8
Again, calculate the value using a calculator.
(c) The range:
The range refers to the horizontal distance traveled by the projectile. It can be calculated using the formula:
Range = initial velocity * cos(angle) * time of flight
Substituting the given values:
Range = 80 * cos(60) * (time of flight from part (a))
(d) The velocity of projection 2 seconds after being fired:
To find the velocity of projection after 2 seconds, we need to break down the projectile motion into horizontal and vertical components.
Horizontal component:
The horizontal velocity remains constant throughout the motion. So, the velocity of projection in the horizontal direction will be the same as the initial velocity: 80 m/s.
Vertical component:
The vertical velocity changes due to the effect of gravity. After 2 seconds, the vertical velocity can be calculated using the formula:
Vertical component = initial velocity * sin(angle) - g * time
Substituting the given values:
Initial velocity = 80 m/s
Angle = 60 degrees
g = 9.8 m/s^2
Time = 2 seconds
Calculate the value using a calculator.
Using the horizontal (80 m/s) and vertical components, you can find the velocity of projection 2 seconds after being fired by using the Pythagorean theorem:
Velocity of projection 2 seconds after being fired = square root of (horizontal component^2 + vertical component^2)
For a, using g = 9.80 m/s^2, I get
T = 2 u sin 60/g = 14.14 s. If I use g = 9.81 m/s^2, I get 14.12 s.
This leads to slightly different answers to b) and c) than were obtained by vishesh
c) Use
R = u cos 60 * T