Find its maximum height and initial velocity

In summary, the formula for finding the maximum height of an object is h = (v^2sin^2θ) / (2g), where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. The initial velocity of an object can be calculated using the formula v = √(2gh) / sinθ, and the maximum height cannot be negative. Air resistance can decrease the maximum height of an object, and there is another formula for calculating the maximum height without knowing the initial velocity, which requires knowledge of the final velocity at the highest point.
  • #1
wolfson_1123
14
0
Hello i have been able to do 7 out of 8 question on my linear motion questions, but this last question number 8, is proving difficult. I don't know whether the tutor has made a mistake (as the answers are typed at the bottom) so if you could be of help i would be very glad ty.

I am using s = u.t + 0.5.a.t^2

and v = U + a.t

but neither bring up the correct answers:

8. A pistol pellet is fired vertically upwards and lands back at its firing point
8 seconds later. Neglecting air resistance, and assuming the acceleration due to gravity is g = 9.81 m/s2 downwards ! find its maximum height and initial velocity.
[answers: 78.5 m , 39.2 m/s]

Ty every so much :-)
 
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  • #2
Welcome to PF :biggrin:
The bullet starts with velocity v,slows down due to gravity,and attains v=0 at max height.Then it picks up speed(due to gravity) and reaches down with total velocity v.
So time taken to attain v=0 is 8/2=4s.
I plugged this into the eqn and got the given answer.
Similarly,height reached is when velocity becomes 0,I got the given answer with the eqn you gave.
I think you tried t=8s.I hope you understood.
regards
 
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FAQ: Find its maximum height and initial velocity

What is the formula for finding the maximum height of an object?

The formula for finding the maximum height of an object is:
h = (v2sin2θ) / (2g), where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

How do you calculate the initial velocity of an object?

The initial velocity of an object can be calculated by using the formula:
v = √(2gh) / sinθ, where v is the initial velocity, h is the maximum height, θ is the angle of launch, and g is the acceleration due to gravity.

Can the maximum height of an object be negative?

No, the maximum height of an object cannot be negative. It represents the highest point the object reaches, and by definition, it cannot be below the starting point.

How does air resistance affect the maximum height of an object?

Air resistance can decrease the maximum height of an object. As the object moves through the air, it experiences a force in the opposite direction of its motion, which can decrease its velocity and thus its maximum height.

Is there a way to find the maximum height of an object without knowing the initial velocity?

Yes, the maximum height can also be calculated using the formula:
h = (v2sin2θ) / (2g), where h is the maximum height, v is the final velocity at the highest point, θ is the angle of launch, and g is the acceleration due to gravity. This formula does not require knowledge of the initial velocity, but it does require knowing the final velocity at the highest point, which can be found using the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time it takes to reach the highest point.

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