an object is projected with a velocity of 10m/s from the ground level at an angle to the vertically, the total time of flight of projectile os 10secs. calculate angle when (g=10m/s) show workings
To calculate the angle at which the object was projected, we can use the formula for the total time of flight of a projectile:
Time of flight = 2 * (Velocity * sin(angle)) / g
Given that the time of flight is 10 seconds and the acceleration due to gravity is 10 m/s², we can substitute these values into the formula:
10 = 2 * (10 * sin(angle)) / 10
Simplifying further:
1 = sin(angle)
To find the angle, we take the inverse sine (sin⁻¹) of both sides:
angle = sin⁻¹(1)
The inverse sine of 1 is equal to 90 degrees. Therefore, the angle at which the object was projected is 90 degrees.
To calculate the angle at which the object is projected, we can use the equation for the total time of flight of a projectile. The formula is given as:
\(\text{Time of flight} = \frac{2 \times \text{Initial velocity} \times \sin(\text{angle of projection})}{\text{Acceleration due to gravity}}\)
Given the following information:
Initial velocity (\(u\)) = 10 m/s
Total time of flight = 10 s
Acceleration due to gravity (\(g\)) = 10 m/s^2
Let's substitute these values into the equation and solve for the angle of projection (\(\theta\)).
Using the rearranged formula:
\(\sin(\text{angle of projection}) = \frac{\text{Total time of flight} \times \text{Acceleration due to gravity}}{2 \times \text{Initial velocity}}\)
\(\sin(\theta) = \frac{10 \times 10}{2 \times 10}\)
\(\sin(\theta) = 0.5\)
To find the angle (\(\theta\)), we need to take the inverse sine (sin^-1) of 0.5:
\(\theta = \sin^{-1}(0.5)\)
Using a calculator, we find:
\(\theta ≈ 30°\)
Therefore, the angle of projection when the total time of flight is 10 seconds is approximately 30 degrees.
5 seconds up, 5 seconds down
do vertical problem first with Vi = initial velocity component up
v = Vi - g t
at top v = 0
0 = Vi - 10 t
but t = 5 seconds
so
Vi = 50 m/s
IF YOU LAUNCH AT 10 m/s, YOU CAN NOT STAY IN THE AIR TEN SECONDS!