The magnitude of acceleration is given by the formula g(t)= 14sin(t) + 19 in fee

Question

The magnitude of acceleration is given by the formula g(t)= 14sin(t) + 19 in feet per sec2 and it is in adownward direction. A projectile is fired from ground level with aspeed of 100 ft/sec at an elevation angle of 0.55 radians. What isthe speed of the projectile at t=1 seconds? Thanks The magnitude of acceleration is given by the formula g(t)= 14sin(t) + 19 in feet per sec2 and it is in adownward direction. A projectile is fired from ground level with aspeed of 100 ft/sec at an elevation angle of 0.55 radians. What isthe speed of the projectile at t=1 seconds? Thanks

Explanation / Answer

vertical direction: a(t) = -(14sint + 19) ft/s2, initialvelocity v0y = 100sin(0.55) ft/s, t = 1 final velocity vy = v0y - (14sint +19) dt,   (integral limit: 0 to 1) vy = v0y + 14cost - 19t, input integrationlimits, vy = 100sin(0.55) + 14cos(1) - 14cos(0) - 19 = 26.8ft/s horizontal: vx = 100cos(0.55) = 85.3 ft/s speed = 89.4 ft/s

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