If a projectile is fired with initial velocity of an angle 90° calculate
I) time of flight
II)height
III) range of flight
Take g=9.8m/s-2
once you decide on the initial velocity v0, then
v = v0 - 9.8t
h = v0*t - 4.9t^2
i) find t when v=0 -- that is how long it takes to go up and stop. That is 1/2 the time of flight.
ii) find h(t) from (i)
(iii) range=0, since it comes back straight down
To calculate the time of flight, height, and range of flight of a projectile fired at an angle of 90°, we can use the following formulas:
I) Time of flight (T) = 2 * (Initial velocity (Vo) * sin(angle θ) / g)
II) Maximum height (H) = (Vo^2 * sin^2(angle θ)) / (2 * g)
III) Range of flight (R) = (Vo^2 * sin(2 * angle θ)) / g
Let's calculate each step by step:
I) Time of flight (T):
Since the angle is 90°, the vertical velocity component is zero. Therefore, the time of flight can be calculated as:
2 * (Vo * sin(90°) / g) = 2 * (Vo / g)
II) Maximum height (H):
The maximum height occurs when the vertical velocity component becomes zero. Hence, the maximum height can be calculated as:
(Vo^2 * sin^2(90°)) / (2 * g) = (Vo^2) / (2 * g)
III) Range of flight (R):
Since the angle is 90°, the horizontal velocity component is maximum and remains constant throughout the flight. Hence, the range of flight can be calculated as:
(Vo^2 * sin(2 * 90°)) / g = (Vo^2 * sin(180°)) / g = (Vo^2 * 0) / g = 0
Thus, the range of flight in this case is zero.
To summarize:
I) Time of flight (T) = 2 * (Vo / g)
II) Maximum height (H) = (Vo^2) / (2 * g)
III) Range of flight (R) = 0
To calculate the time of flight, height, and range of a projectile fired at an angle of 90° (straight up), we can use the following formulas:
I) Time of Flight:
The time of flight of a projectile is the total time it takes for the projectile to return to the same height from where it was launched. In this case, when a projectile is fired straight up, it will reach its highest point and then fall back down. The time taken to reach the highest point is half of the total time of flight.
To calculate the time of flight (T), we can use the equation:
T = 2 * (vertical component of initial velocity) / acceleration due to gravity
Since the angle is 90°, the initial velocity has no horizontal component, only a vertical component. Therefore, the vertical component of initial velocity is the magnitude of the initial velocity.
Given:
Initial velocity (u) = magnitude of the initial velocity = ? (not provided)
Acceleration due to gravity (g) = 9.8 m/s²
II) Height:
The height of the projectile is the maximum height it reaches above its initial launch height.
To calculate the height (H), we can use the equation:
H = (vertical component of initial velocity)² / (2 * acceleration due to gravity)
Given:
Initial velocity (u) = magnitude of the initial velocity = ? (not provided)
Acceleration due to gravity (g) = 9.8 m/s²
III) Range of Flight:
The range of flight is the horizontal distance traveled by the projectile before hitting the ground.
Since the angle is 90°, the projectile will only have a vertical component of motion and no horizontal motion. Therefore, the range of flight is zero.
So, to summarize:
I) To calculate T - Time of Flight: T = 2 * (u) / g
II) To calculate H - Height: H = (u²) / (2 * g)
III) To calculate range - Range of Flight: Range = 0
Please provide the magnitude of the initial velocity (u) to calculate the time of flight and the height.