A projectile spends a total of 20 seconds in the air. It reaches a peak height of 8 meters. How long does it take to reach it's peak height
It spends 10 seconds going up and 10 seconds coming down. You don't need to know the peak height to conclude that.
The initial vertical velocity component (Vo sinA) could be calculated from the numbers they gave you.
To find out how long it takes for the projectile to reach its peak height, we need to use the equation of motion for vertical motion.
We know that the projectile reaches a peak height of 8 meters, which means its vertical displacement is 8 meters. The equation for vertical displacement is given by:
y = u * t + (1/2) * a * t^2
Where:
y = vertical displacement (8 meters in this case)
u = initial vertical velocity (unknown)
t = time taken to reach peak height (unknown)
a = acceleration due to gravity (-9.8 m/s^2, assuming upward as positive)
The initial vertical velocity (u) is the velocity of the projectile at the moment it is launched. Since we do not know the launch velocity, we cannot directly solve for the time taken to reach the peak height using this equation.
However, we can make use of the fact that the total time of flight is given as 20 seconds. The time taken to reach the peak height is half of the total time of flight since the projectile spends an equal amount of time going up and coming down. Therefore, the time taken to reach the peak height would be:
t = (20 seconds) / 2
t = 10 seconds
So, it takes 10 seconds for the projectile to reach its peak height.