A ball is shot horizontally at a speed of 10 m/s from a height
of 2 meters. How long is the ball in the air and how far horizontally does it travel before
it hits the ground?
1) find the time it takes to fall 2 meters.
2=1/2 g t^2 find t.
2) how far does the ball go in t seconds horizontally.
distance= 10m/s*t
To find how long the ball is in the air, we can use the equation of motion:
š = š£šššš” + 0.5šš”Ā²
In this case, the initial vertical velocity (š£ššš) is 0 m/s since the ball is shot horizontally. The acceleration (š) due to gravity is -9.8 m/sĀ² (taking downward as negative).
The vertical displacement (š) is -2 meters since the ball starts at a height of 2 meters and falls down.
Substituting the values into the equation, we have:
-2 = 0(š”) + 0.5(-9.8)(š”)Ā²
Simplifying the equation, we get:
-2 = -4.9š”Ā²
Rearranging the equation, we have:
š”Ā² = 2/4.9
š”Ā² = 0.408
Taking the square root of both sides, we find:
š” ā 0.64 seconds
Therefore, the ball is in the air for approximately 0.64 seconds.
To find how far horizontally the ball travels before hitting the ground, we can use the equation:
š = š£āšššš§ššš”šš Ć š”
The horizontal velocity (š£āšššš§ššš”šš) remains constant throughout the motion and is equal to 10 m/s, as given in the problem.
Substituting the values into the equation, we have:
š = 10 Ć 0.64
š ā 6.4 meters
Therefore, the ball travels approximately 6.4 meters horizontally before hitting the ground.