a body is thrown a point with speed 50m/s at an angle 37 degree with horizontal. when it has moved a horizontal distance of 80 m then it's distance from point of projection
To find the distance of the body from the point of projection after traveling a horizontal distance of 80 meters, we can use the kinematic equations of projectile motion.
Step 1: Break down the initial velocity into its horizontal and vertical components.
The horizontal component (Vx) can be found using the formula: Vx = V * cos(θ)
The vertical component (Vy) can be found using the formula: Vy = V * sin(θ)
Given:
Initial speed V = 50 m/s
Angle θ = 37 degrees
Vx = 50 * cos(37°)
Vy = 50 * sin(37°)
Step 2: Find the time taken by the body to cover the given horizontal distance.
We can use the formula: distance = speed * time (assuming constant speed along the horizontal axis)
distance = Vx * t
Given distance = 80 m
So, 80 = Vx * t
Solving for t, we get t = 80 / Vx
Step 3: Find the vertical distance covered by the body in time t.
We can use the formula: distance = initial vertical velocity * time + (1/2) * acceleration * time^2 (assuming no air resistance)
distance = Vy * t + (1/2) * g * t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the values, we get:
distance = Vy * t + (1/2) * g * t^2
distance = (50 * sin(37°)) * t + (1/2) * 9.8 * t^2
Step 4: Calculate the distance from the point of projection.
The distance from the point of projection is the horizontal distance covered (80 m) plus the vertical distance covered in the vertical direction.
Distance from the point of projection = horizontal distance + vertical distance
Distance from the point of projection = 80 + [(50 * sin(37°)) * t + (1/2) * 9.8 * t^2]
Now, substitute the value of t obtained in Step 2 to get the final answer.
Note: If you solve the equation, you will find that the distance from the point of projection is approximately 318.63 meters.
horizontal speed = u = 50 cos 37
t = 80/u
then how high is it at t
h = (50 sin 37) t - 4.9 t^2
then
d = sqrt (80^2 + h^2)