Question

If initial speed of an object is v = 1340 ft/s. When it hits a wall it sinks in 5 in. If velocity of object while in the wall is v = vo – kx (ft/s) and (x in feet), find a) the initial acceleration when object enters wall and b) time needed to sink 4.5 in.

Answer 1

Answer:

(a).    a = -4309105 m/s

(b).   t = 7.158 × 10 ⁻⁴ sec

Explanation:

from the question, given that;

initial speed (Vo) = 1340ft/s

 x = 5 in = 0.4167 ft (conversion factor)

 but V = (Vo - Kx)

where a = V dv/dx

∴ a = (Vo-Kx) d/dx (Vo-Kx)

  a = (Vo-Kx) (-K)│x=o

  a = -KVo

therefore, 0 = 1340 - K (0.4167)

K = 1340/ 0.4167 = 3215.75 sec⁻¹

 a = - 3215.75 × 1340

which gives a = -4309105 m/s

(b). given that x = 4.5 in = 0.375 ft

      V = dx/dt = V₀ - Kx

       = $\int\limit^{0.375} _0 {(1/1340 - 3215.75x)} dx = \int\limits^t_0 {} \, dt$

    =  - 1/3215.75 $\lim_{0 \to \00.375} (1340-3215.75x)$

        t = 7.158 × 10 ⁻⁴ sec