The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of power roller skates, which provide a constant horizontal acceleration of 15 m/s2, as shown in Figure P3.73. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff. (a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have to reach the cliff before the coyote. (b) If the cliff is 100 m above the base of a canyon, find where the coyote lands in the canyon. (Assume his skates are still in operation when he is in &ldquo;flight&rdquo; and that his horizontal component of acceleration remains constant at 15 m/s2.)

Question

The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of power roller skates, which provide a constant horizontal acceleration of 15 m/s2, as shown in Figure P3.73. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff. (a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have to reach the cliff before the coyote. (b) If the cliff is 100 m above the base of a canyon, find where the coyote lands in the canyon. (Assume his skates are still in operation when he is in &amp;ldquo;flight&amp;rdquo; and that his horizontal component of acceleration remains constant at 15 m/s2.)

Vasquez · Accepted Answer

(a) Derive the expression for the minimum time required for the coyote to travel a distance of Δx from the cliff.The distance travelled by the coyote is,Δx=v0xt+12axt2Here v0x is the initial horizontal velocity and ax is the horizontal acceleration of the coyote, and t is the time to cover the distance Δx.The initial velocity og the coyote is zero.v0x=0 m/sSubstitute 0 m/s for v0x in the equation Δx=v0xt+12axt2 and solve for t.Δx=(0 m/s)t+12axt2t=2ΔxaxThe roadrunner is moving with a constant speed. Hence, the minimum speed to reach the cliff is as follows.vmin=ΔxtSubstitute 2Δxax for t.vmin=Δx2Δxax=axΔx2Substitute 15 m/s2 for ax and 70 m for Δxvmin=(15 m/s2)(70 m)2=23 m/sHence, the required minimum speed of the roadrunner is 23 m/sb) The initial velocity of the coyote when it goes over the cliff is equal to the horizontal velocity.v0x=axtSubstitute 2Δxax for t.v0x=ax2Δxax=2axΔxThe time taken to cover the vertical height of the cliff is,t′=2ΔyayHere Δy is vertical heisght of the cliff.Therefore, the horizontal displacement of the fall of the coyote is,Δx=v0xt+12axt2Substitute  =2axΔx for v_{0x} and 2Δyay for t′.Δx=2axΔx(2Δyay)+12ax(2Δyay)2 Substitute 15 m/s2 for ax and 70 m for Δx, −100 m for Δy, and −9.80 m/s2 for ayΔx=2(15 m/s)(70 m)(2(−100 m)−9.80 m/s2)+12(15 m/s)(2(−100 m)−9.80 m/s2)2=3.6×102 mHence, the reauired dispplacement is 3.6×102 m

The determined Wile E. Coyote is out once

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