An object is hurled downward with an initial velocity of 15 m/s from a height of 52 m.
How long does the object take to hit the ground?
What speed does the object strike?
How long does the object take to hit the ground?
What speed does the object strike?
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With gravitational acceleration equal 9.81 m/s²
s(t) = 52 - 15t - 4.905t², t ≥ 0
v(t) = -15 - 9.81t
At impact, s(t) = 0
4.905t² + 15 t - 52 = 0
Time of impact = t = [-15 + √(15² + 4*52*4.905)]/9.81 = 2.07 seconds (the negative solution of the quadratic equation is discarded since the time domain doesn't include negative values of t)
Speed at impact = v(2.07) = -15 - 9.81*2.07 = -35.3 m/s (negative sign indicates the direction of the velocity vector is downward)
s(t) = 52 - 15t - 4.905t², t ≥ 0
v(t) = -15 - 9.81t
At impact, s(t) = 0
4.905t² + 15 t - 52 = 0
Time of impact = t = [-15 + √(15² + 4*52*4.905)]/9.81 = 2.07 seconds (the negative solution of the quadratic equation is discarded since the time domain doesn't include negative values of t)
Speed at impact = v(2.07) = -15 - 9.81*2.07 = -35.3 m/s (negative sign indicates the direction of the velocity vector is downward)
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d = v0 * t + (1/2)a t^2.
Plug in the known values of d, v0 and a, and solve the quadratic equation for t.
v = v0 + at.
Plug in the known values of v0, a and t.
Or use this one: v^2 = v0^2 + 2ad with the known values of v0, a and d. You could then use that value of v in v = v0 + at to find t.
Plug in the known values of d, v0 and a, and solve the quadratic equation for t.
v = v0 + at.
Plug in the known values of v0, a and t.
Or use this one: v^2 = v0^2 + 2ad with the known values of v0, a and d. You could then use that value of v in v = v0 + at to find t.