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

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 .

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?

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gneill
Mentor
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?

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.