Basic projectile motion question

[gorays1414]

If I can throw a ball on a level field with a range of 15 m, how high would the ball travel if the same throw was made vertically?

Using the range equation, I found the velocity to be 12.1 m/s, and the final answer to be 7.5m. Is this correct?

 

[Adithyan]

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]

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

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]

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.

The formula for maximum range of a projectile motion is $\frac{u^{2}}{g}$ ('u' being the velocity) whereas the maximum attainable height by a ball thrown vertically upwards = $\frac{u^{2}}{2g}$ (This can be derived using the kinematical equations). So the latter is half of the former. Got it now?

 

[gorays1414]

The formula for maximum range of a projectile motion is $\frac{u^{2}}{g}$ ('u' being the velocity) whereas the maximum attainable height by a ball thrown vertically upwards = $\frac{u^{2}}{2g}$ (This can be derived using the kinematical equations). So the latter is half of the former. Got it now?

Got it, thanks so much.