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Finding the time that a ball is in air, using projectile motion kinematics.

  • Thread starter garcia1
  • Start date
27
0
1. Homework Statement
A ball is thrown from the top of a building upward at an angle of 35◦ to the horizontal and with an initial speed of 10 m/s. The ball is thrown at a height of 43 m above the ground.
How long is the ball “in flight”? The acceleration due to gravity is 9.8 m/s2 .
Answer in units of s.


2. Homework Equations
Kinematics equations and their vector components


3. The Attempt at a Solution

I wanted to try breaking this problem up into two different segments and solve for the time of each of them.

segment one, I wanted to find the time of the ball as it arcs at the angle of 35 degrees until it begins to descend past the height from which it was thrown.

I decided to find the y component of the velocity by using trigonometry. I used the equation sin(35) = Vy/10m/s and solved for Vy, getting 5.736.

Since this velocity points downward as it ascends, I labeled this velocity as the Vf of this segment, -5.736m/s.

Using kinematics equation Vf = Vo +at, I solved for t, using Vo as the point where Vy is at the top, with no movement, 0m/s.

My answer was -.5847s, so I'm not sure if I messed up on my conceptual layout or if I can just interpret this segment as a positive, since time can only be positive.

Past this, I'm pretty lost. Any thoughts?
 

Answers and Replies

gneill
Mentor
20,538
2,628
There's really no need to break the motion down into segments. The basic kinematics equation covers the whole trajectory.

You have an initial y-velocity (you found this already), and an initial height (43m). What's the equation of motion for the motion in the vertical direction?
 
50
0
My answer was -.5847s, so I'm not sure if I messed up on my conceptual layout or if I can just interpret this segment as a positive, since time can only be positive.
Remember that the gravity will be negative as the ball is travelling upwards.

I haven't seen your workings, but I think you put gravity as positive, and hence got a negative value for time.
 

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