Adithyan said:Yes it is 7.5m assuming 15m is the maximum attainable range with that velocity.
P.S: You could have solved this question without finding the velocity (I think you get it)
Regards!
ADI
gorays1414 said:How could you have solved without finding the velocity? I get that there must be some type of relationship between the height and the maximum range, but I'm not sure I understand exactly what it is.
Adithyan said:The formula for maximum range of a projectile motion is [itex] \frac{u^{2}}{g}[/itex] ('u' being the velocity) whereas the maximum attainable height by a ball thrown vertically upwards = [itex] \frac{u^{2}}{2g}[/itex] (This can be derived using the kinematical equations). So the latter is half of the former. Got it now?
Projectile motion is the motion of an object through the air that is affected by gravity. It can be described as a parabolic path, where the object has both a horizontal and vertical component to its motion.
The key factors that affect projectile motion are the initial velocity, angle of launch, and the acceleration due to gravity. These factors determine the trajectory and range of the projectile.
The velocity of a projectile can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time.
The horizontal component of projectile motion remains constant, as there is no force acting on the object in the horizontal direction. The vertical component, however, is affected by gravity and changes throughout the motion.
The angle of launch affects the range of a projectile as it determines the balance between the horizontal and vertical components of the motion. The optimal angle for maximum range is 45 degrees.