Okay, so I came across this interesting problem:
A football is kicked at a 50 degree angle to the horizontal and travels a horizontal distance of 20m before hitting the ground. What is its initial speed?
Here's my working:
Now when we consider the horizontal component of the football's motion, s=ut. Thus,
(u cos50°)t= 20
When we consider the vertical component of the football's motion, v= u+at. Thus,
0= (u sin50°)-g(20/u cos50°)
u sin50°= 20g/u cos50°
20= (u²sin50°cos50°)/g
= u²sin100°/2g --->since sin2θ= 2sinθcosθ
Thus, shouldn't the formula for range be u²sin2θ/2g? Why is it u²sin2θ/g? As you can see from the way I've worded the question, it's not the answer I'm concerned about. Rather, it's about the formula for the range of the football. Please explain to me where I've gone wrong.
A football is kicked at a 50 degree angle to the horizontal and travels a horizontal distance of 20m before hitting the ground. What is its initial speed?
Here's my working:
Now when we consider the horizontal component of the football's motion, s=ut. Thus,
(u cos50°)t= 20
When we consider the vertical component of the football's motion, v= u+at. Thus,
0= (u sin50°)-g(20/u cos50°)
u sin50°= 20g/u cos50°
20= (u²sin50°cos50°)/g
= u²sin100°/2g --->since sin2θ= 2sinθcosθ
Thus, shouldn't the formula for range be u²sin2θ/2g? Why is it u²sin2θ/g? As you can see from the way I've worded the question, it's not the answer I'm concerned about. Rather, it's about the formula for the range of the football. Please explain to me where I've gone wrong.
-
Your error is as under.
You considered v = u - gt
Now, v is the velocity at the highest point.
So, if the total time for flight = t, time to reach velocity v = t/2, whereas you have taken t which results in the error. With this correction, range will be u²sin2θ/g.
You considered v = u - gt
Now, v is the velocity at the highest point.
So, if the total time for flight = t, time to reach velocity v = t/2, whereas you have taken t which results in the error. With this correction, range will be u²sin2θ/g.