A ball thrown with a speed of 100m/s,attains a height of 150m (g is 9.8m/s2.Calculate (i) time of flight (ii)angle of projection
Hi Abdul,time of flight can be calculated by (2h/g)^1/2 which comes to be 30.6s.
how electron and proton can deflect with same radius
Usama, what type of deflection you are talking about. Deflection in an electrical or magnetic field?
Y^2 = Yo^2 + 2g*h.
0 = Yo^2 + (-19.6)*150,
Yo = 54.2 m/s = Initial ver. component.
1. Y = Yo + g*Tr.
0 = 54.2 -9.8Tr,
Tr = 5.53 s. = Rise time.
Tf = Tr = 5.53 s. = Fall time.
Tr+Tf = 5.53 + 5.53 = 11.1 s. = Time of flight.
2. Vo = 100m/s[Ao].
Yo = 100*sin A,
54.2 = 100*sin A,
A = 32.8o.
To calculate the time of flight and angle of projection, we can use the equations of motion for projectile motion.
(i) Time of Flight:
The time of flight is the total time taken by the projectile to reach its maximum height and return to the same height. We can calculate it using the equation:
time = (2 * vertical velocity) / g
In this case, the initial vertical velocity is zero because at the maximum height the velocity becomes zero. Also, the final vertical velocity is negative because the ball returns to the same height. So, we can rewrite the equation as:
time = (-2 * vertical velocity) / g
Here, the vertical velocity can be calculated by using the equation of motion for the vertical direction:
final vertical velocity^2 = initial vertical velocity^2 + 2 * g * height
By substituting the given values:
final vertical velocity^2 = 0 + 2 * 9.8 * 150
final vertical velocity^2 = 2940
final vertical velocity = √2940
final vertical velocity ≈ 54.09 m/s
Now, substitute this value into the equation for time of flight:
time = (-2 * vertical velocity) / g
time = (-2 * 54.09) / 9.8
time ≈ -5.53 s (Note: The negative sign indicates that the ball is moving downward.)
So, the time of flight is approximately 5.53 seconds.
(ii) Angle of Projection:
The angle of projection is the angle at which the ball is thrown with respect to the horizontal. We can calculate it using the equation:
angle = arctan(vertical velocity / horizontal velocity)
Here, the vertical velocity can be calculated as described earlier. The horizontal velocity is the initial speed of the ball, which is given as 100 m/s.
angle = arctan(54.09 / 100)
angle ≈ 28.55 degrees
So, the angle of projection is approximately 28.55 degrees.