A projectile is thrown from the top of a tower anf strikes the ground after 3sec at angle of 45° with horizontal . Find height of tower and speed with which the projectile was projected.
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To find the height of the tower and the speed at which the projectile was projected, we can use the equations of motion for projectile motion.
First, let's find the horizontal component of the initial velocity of the projectile.
Given that the projectile strikes the ground after 3 seconds with an angle of 45 degrees with the horizontal, we can find the horizontal component of the velocity using the equation:
Vx = V * cos(θ)
where Vx is the horizontal component of the velocity, V is the initial velocity of the projectile, and θ is the angle of projection.
Since the angle of projection is 45 degrees and the horizontal component of the velocity is Vx, the equation becomes:
Vx = V * cos(45°)
Next, let's find the vertical component of the initial velocity of the projectile.
Using the same equation, we can find the vertical component of the velocity:
Vy = V * sin(θ)
where Vy is the vertical component of the velocity.
Since the angle of projection is 45 degrees and the vertical component of the velocity is Vy, the equation becomes:
Vy = V * sin(45°)
Now, let's use the equations of motion to find the height of the tower.
To calculate the height of the tower, we can use the equation:
h = Vy * t - (1/2) * g * t^2
where h is the height of the tower, Vy is the vertical component of the velocity, t is the time of flight, and g is the acceleration due to gravity.
Since we are given that the projectile strikes the ground after 3 seconds, we can substitute the values into the equation:
h = Vy * 3 - (1/2) * g * (3^2)
Now, let's find the speed at which the projectile was projected.
The speed at which the projectile was projected is the magnitude of the initial velocity, which can be calculated using the Pythagorean theorem:
V = sqrt(Vx^2 + Vy^2)
Once we have the value of V, we can calculate the speed at which the projectile was projected.
I hope this explanation helps you understand how to find the height of the tower and the speed at which the projectile was projected.