i was wondering if i did this right
A cannon ball is shot from a cannon on top of a hill that is 73.5 meters above sea level. The cannon ball leaves the cannon with a velocity of 9.8 m/s. Write and solve a quadratic equation to determine when the cannon ball will reach sea level.
0 = -4.9t² + 9.8t + 73.5
0 = -4.9(t² - 2t - 15)
0 = -4.9(t - 5)(t + 3)
t - 5 = 0 and t + 3 = 0
t = {5,-3}
t = 5 since t = -3 is not acceptable negative value.
Hence, the cannon ball will reach sea level at 5 seconds.
Did you shoot the cannon ball while standing on one leg? Because that's some impressive balance!
But back to your question, you did it right! Your quadratic equation is correct. It seems like you've mastered the art of throwing cannon balls (at least mathematically). According to your calculation, the cannon ball will reach sea level after 5 seconds. Just remember, in real life, it may take a little longer due to factors like air resistance and gravity. So keep your eyes on the sky and watch out for falling cannon balls!
Yes, you did it correctly!
You correctly determined the quadratic equation to be:
0 = -4.9t² + 9.8t + 73.5
Then, you factored the equation:
0 = -4.9(t² - 2t - 15)
0 = -4.9(t - 5)(t + 3)
You found two values for t that make the equation equal to zero:
t - 5 = 0 and t + 3 = 0
Finally, you determined that t = 5, since t = -3 is not an acceptable negative value.
Therefore, the cannonball will reach sea level in 5 seconds. Well done!
Yes, you have done it correctly. To determine when the cannonball will reach sea level, we need to use the equation of motion for vertical motion, which is given by:
h(t) = -4.9t² + v₀t + h₀
Where:
h(t) is the height of the cannonball at time t
v₀ is the initial velocity of the cannonball
h₀ is the initial height of the cannonball
In this case, the initial height (h₀) is 73.5 meters above sea level and the initial velocity (v₀) is 9.8 m/s. Since we want to find when the cannonball reaches sea level, we set h(t) to 0:
0 = -4.9t² + 9.8t + 73.5
Now, to solve this quadratic equation, we can factor it or use the quadratic formula. Factoring is the easier method in this case. It seems you made a small mistake in factoring. The correct factorization is:
0 = -4.9(t² - 2t - 15)
0 = -4.9(t - 5)(t + 3)
Then, we find the values of t that make the equation equal to zero by setting each factor equal to zero:
t - 5 = 0 and t + 3 = 0
Solving these equations, we find that:
t = 5 for the cannonball to reach sea level.
So, you have done it correctly. The cannonball will reach sea level after 5 seconds. Well done!