Which parameter of a projectile depends on the horizontal as well as the vertical component of velocity of projection?
distance traveled.
Which parameter of a projectile depends on the horizontal as well as the vertical component of velocity of projection?
The range or horizontal displacement of a projectile depends on both the horizontal and vertical components of velocity.
While attempting a landing on the moon, astronauts had to change their landing site and land at a spot that was 4 kilometers away from the original site. Assuming that they were at a height of 137 meters, calculate the horizontal velocity of the spacecraft during touchdown if it lands in a free-fall mode without using retro engines. Consider gravity = 1.63 meters/second2.
To calculate the horizontal velocity of the spacecraft during touchdown, we can use the equation:
distance = velocity x time
In this case, we know the distance (4 kilometers = 4000 meters) and the height (137 meters). We can assume that the time of flight is the same for both the horizontal and vertical components of motion, as the spacecraft is in free-fall mode without using retro engines.
First, we can calculate the time of flight using the vertical motion equation:
h = (1/2)gt^2
Where h is the height, g is the acceleration due to gravity, and t is the time of flight.
Plugging in the values, we have:
137 = (1/2)(1.63) t^2
274 = (1.63) t^2
t^2 = 274 / 1.63
t^2 = 168.22
t ≈ √168.22
t ≈ 12.98 seconds
Now, let's calculate the horizontal velocity using the equation:
distance = velocity x time
4000 = velocity * 12.98
velocity = 4000 / 12.98
velocity ≈ 308.32 meters/second
Therefore, the horizontal velocity of the spacecraft during touchdown is approximately 308.32 meters/second.
The parameter of a projectile that depends on both the horizontal and vertical component of velocity of projection is the range.
The range of a projectile is the horizontal distance covered by the projectile from its initial position to the point where it hits the ground. It is influenced by both the horizontal and vertical components of velocity.
To understand why the range depends on both components, we need to break down the projectile motion into its horizontal and vertical components.
The horizontal component of velocity is responsible for the projectile's motion in the x-axis, while the vertical component of velocity is responsible for its motion in the y-axis.
A projectile follows a parabolic trajectory, and its motion in the vertical direction is influenced by the force of gravity. Gravity affects the projectile's vertical motion by causing it to accelerate downward. This acceleration gradually decreases the vertical component of its velocity until it reaches zero at the highest point of the trajectory (peak height).
The horizontal component of velocity, on the other hand, remains constant throughout the motion as there are no horizontal forces acting on the projectile (assuming there is no air resistance).
Since the horizontal component of velocity remains constant, the range only depends on the time of flight and the horizontal velocity. The time of flight is determined by the vertical component of velocity and the acceleration due to gravity. The greater the vertical component of velocity or the greater the time of flight, the longer the distance traveled horizontally, resulting in a longer range.
In summary, the range of a projectile depends on both the horizontal and vertical components of velocity because the horizontal component determines the constant velocity in the x-axis, while the vertical component influences the time of flight and, therefore, the duration over which the constant horizontal velocity is maintained.