a ball is thrown upward. its initial verticle component of velocity is 10 m/s and its initial horizontal component of velocity is 2 m/s. what is the ball's speed 10 s later?
the vertical component:
Vf=10-g*10=-88m/s
Vh=2
so add those vertical and horizontal components...
v=sqrt(2^2 + 88^2)
To find the ball's speed 10 seconds later, we need to first calculate its final vertical and horizontal velocities at that time and then use those values to find the overall speed.
The initial vertical component of velocity is given as 10 m/s. Since the ball is thrown upward, we can assume the acceleration due to gravity (-9.8 m/s^2) will act against its vertical velocity. After 10 seconds, the final vertical velocity can be calculated using the equation:
Final vertical velocity = initial vertical velocity + (acceleration due to gravity × time)
Final vertical velocity = 10 m/s + (-9.8 m/s^2 × 10 s)
Final vertical velocity = -98 m/s
The negative sign indicates that the ball is moving downward after 10 seconds.
As for the horizontal component of velocity, it remains constant throughout the ball's motion. Therefore, the horizontal component of velocity after 10 seconds will still be 2 m/s.
To find the overall speed, we can use the Pythagorean theorem:
Speed = √((vertical velocity)^2 + (horizontal velocity)^2)
Speed = √((-98 m/s)^2 + (2 m/s)^2)
Speed = √(9604 m^2/s^2 + 4 m^2/s^2)
Speed = √(9608 m^2/s^2)
Speed ≈ 98.02 m/s
Therefore, the ball's speed 10 seconds later would be approximately 98.02 m/s.