A particle is projected from horizontal making an angle 60dgree with initial velocity u .if time taken to the particle to make an angle 45dgree from horizontal is 1.5 sec .then u is?

Question

Answer

Projectile Motion Problem

In this problem, we are given the initial angle and time taken by a particle to make a certain angle. We need to calculate the initial velocity of the particle.

Understanding Projectile Motion

Projectile motion is a type of motion where an object is thrown near the earth's surface and moves along a curved path under the influence of gravity. In this type of motion, we assume that the only force acting on the object is gravity.

Deriving the Equations of Projectile Motion

We can derive the equations of projectile motion using the following assumptions:

The only force acting on the object is gravity.

The acceleration due to gravity is constant and equal to 9.81 m/s^2.

The motion takes place in a plane, usually the x-y plane.

Using these assumptions, we can derive the following equations:

x = u*cos(theta)*t

y = u*sin(theta)*t - (1/2)*g*t^2

v = sqrt(u^2 + 2*g*y)

theta = atan((v*sin(alpha) + g*t)/v*cos(alpha))

where:

x = horizontal distance traveled by the particle

y = vertical distance traveled by the particle

u = initial velocity of the particle

theta = initial angle of projection

t = time taken by the particle

g = acceleration due to gravity

v = final velocity of the particle

alpha = angle of velocity vector with respect to the horizontal

Solving the Problem

In this problem, we are given the initial angle of projection and the time taken by the particle to make an angle of 45 degrees with respect to the horizontal. We need to find the initial velocity of the particle.

Let's assume that the horizontal distance traveled by the particle when it makes an angle of 45 degrees is x. We can then use the following equation to find the time taken by the particle:

x = u*cos(theta)*t

where:

x = horizontal distance traveled by the particle

u = initial velocity of the particle

theta = initial angle of projection

t = time taken by the particle

Substituting the given values, we get:

x = u*cos(60)*1.5

x = 0.75*u

Now, let's find the vertical distance traveled by the particle when it makes an angle of 45 degrees. We can use the following equation:

y = u*sin(theta)*t - (1/2)*g*t^2

where:

Answer

I think may be 75m/s

Answer

2√30m/s

Answer

T = 2usin45/g1.5= 2u 1/root2×g.
By this you get u .

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