A stone is thrown from the top of a tower of height 60m with velocity 40m/s at an angle of 30 degree above the horizontal. Calculatethe time taken by the stone to hit the ground. At what distance from the foot of the tower the stone hits the ground.

Vo = 40m/s[30o].

Xo = 40*Cos30 = 34.64 m/s.
Yo = 40*sin30 = 20 m/s.

Y = Yo + g*Tr.
0 = 20 - 9.8Tr, Tr = 2.04 s.

ha = Yo*Tr + 0.5g*Tr^2.
ha = 20*2.04 - 4.9*2.04^2 = 20.4 m. = Ht. above tower.

h = 20.4 + 60 = 80.4 m. Above gnd.

0.5g*Tf^2 = 80.4.
4.9Tf^2 = 80.4, Tf = 4.05 s. = Fall time.

a. Tr+Tf = 2.04 + 4.05 = 6.09 s. To hit gnd.

b. D = Xo*(Tr+Tf) = 34.64 * 6.09 = 211 m.

To solve this problem, we can break down the motion of the stone into horizontal and vertical components.

1. Vertical Motion:
We know that the initial vertical velocity (Vy) is given by:
Vy = V * sin(theta)
where V is the initial velocity of the stone (40 m/s) and theta is the angle above the horizontal (30 degrees).
Substituting the values, we have:
Vy = 40 * sin(30)
Vy = 20 m/s

The vertical displacement (sy) of the stone can be determined using the formula:
sy = Vyi * t + (1/2) * a * t^2
where Vyi is the initial vertical velocity, t is the time taken, and a is the acceleration due to gravity (-9.8 m/s^2).
Since the stone is thrown upwards and then falls down, the value of a will be negative.
Thus, we have:
sy = 20 * t - (1/2) * 9.8 * t^2
sy = 20t - 4.9t^2

At the time when the stone hits the ground, the vertical displacement (sy) will be equal to -60m (since the negative direction is considered downward).
Substituting this value, we can solve the equation:
-60 = 20t - 4.9t^2

2. Horizontal Motion:
The horizontal displacement (sx) can be determined using the formula:
sx = Vx * t
where Vx is the horizontal velocity, which is given by:
Vx = V * cos(theta)
Substituting the values, we have:
Vx = 40 * cos(30)
Vx = 40 * (√3/2)
Vx = 20√3 m/s

To find the time taken for the stone to hit the ground, we can ignore the effects of air resistance and assume that the time taken for vertical and horizontal motions is the same.
Thus, we can use the time (t) obtained from the vertical motion calculations.

At the time when the stone hits the ground, the horizontal displacement (sx) will be equal to the distance from the foot of the tower (x).
So, we can solve the equation:
x = 20√3 * t

Now, we can solve these two equations to find the values of t and x.